W. 


U.   8.   DEPARTMENT  OP  AGRICULTURE, 
"WEATHER  BUREAU. 


STUDIES  ON  THE  METEOROLOGICAL  EFFECTS  IN  THE  UNITED 
STATES  OF  THE  SOLAR  AND  TERRESTRIAL  PHYSICAL  PROCESSES. 


Reprints  from  the  Monthly  Weather  Review,  December,  1902,  January  and  February,  1903. 


BY 
FRANK  H.  BIGELOW,  M.  A.,  L.  H.  D., 

PROFESSOR  OF  METEOROLOGY. 


PEEP  ABED  UNDEb  THE  DIRECTION  OF 

WILLIS   L.   MOORE, 

CHIEF  U.  S.  WEATHER  BUREAU. 


WASHINGTON  : 
ATHER     BUREAU 

1903. 


W.  B.  No.  290. 


U.   S.   DEPARTMENT  OF  AGRICULTURE, 
WEATHER  BUREAU. 


STUDIES  ON  THE  METEOROLOGICAL  EFFECTS  IN  THE  UNITED 
STATES  OF  THE  SOLAR  AND  TERRESTRIAL  PHYSICAL  PROCESSES. 


Keprints  from  the  Monthly  Weather  Review,  December,  1902,  January  and  February,  1903. 


BY 
FRANK  H.  BIGELOW,  M.  A.,  L.  H.  D. 

PROFESSOR  OF  METEOROLOGY. 


10635 


PREP  ABED  UNDER  THE  DIRECTION  OF 

WILLIS   L.    MOOEE, 

CHIEF  U.  S.  WEATHER  BUREAU. 


WASHINGTON: 

WEATHER     BUREAU 

1903. 


(. 


Errata 


I. — The  semidiurnal  periods  in  the  earth's  atmosphere 

The  double  and  single  diurnal  periods 

The  solar  radiation 

Radiation  function  in  the  normal  spectrum 

Remarks  on  the  solar  constant 

The  terrestrial  radiation 

Explanation  of  the  formation  of  the  two  typos  of  diurnal 
periods  


II. — Synchronous  changes  in  the  solar  and  terrestrial  atmosphere 

General  remarks 

Distribution  in  longitude 

Distribution  in  latitude 

Variations  in  latitude  in  the  11-year  cycle 


III. — The  structure  of  cyclones  and  anticyclones  on  the  3500-foot 

and  10,000-foot  planes  for  the  United  States.  .  .  . 

Examples  of  selected  cyclones 


IV. — The  mechanism  of  counter  currents  of  different  tempera- 
tures in  cyclones  and  anticyclones , 

The  Weather  Bureau  cloud  observations  

The  general  circulation 

The  local  circulation  in  cyclones  and  anticyclones 

The  isobars  and  stream  lines  on  the  sea-level  piano,  the 
3500-foot  plane,  and  the  10,000-foot  piano 

The  mechanism  in  cyclones  and  anticyclones 

Comparison  with  other  observed  configurations 

The  interaction  of  three  thermal  currents 

Examples  of  the  interaction  of  abnormally  cold  and  warm 
strata  

General  results  stated , 


I.  Table  1. — Energy  spectra  at  solar  temperatures  reduced  to 
the  distance  of  the  earth,  expressed  in  units  of 
gram  calories  per  square  centimeter  per  minute. 
2. — Energy  spectra  at  terrestrial  temperatures,  ex- 
pressed in  units  of  gram  calories  per  square 
centimeter  per  minute 

II.  Table  1. — Moan  observed  distribution  in  latitude  during  the 
11-year  solar  cycle.  Solar  prominences 

2. — Mean  observed  distribution  in  latitude  during  the 
11-year  solar  cycle.  Solar  spots  and  facultc  .  .  . 

3. — Italian  observations.  Observed  mean  monthly  dis- 
tribution of  the  solar  prominences 

4. — Observed  mean  monthly  distribution  of  the  solar 
spots  

5. — Observed  mean  monthly  distribution  of  the  solar 

facula; 

IV.  Table  1. — Pressure  and  temperature  gradients  in  English 
measures.  Fall  of  pressure  in  inches  per  100 
feet  

2. — Summary  of  the  data  for  the  Cottage  City  water- 
spout, August  19,  1896 


Page. 

iv 

1 
1 
2 
3 
3 
7 


9 

9 

9 

11 

14 


20 
21 


25 
25 
25 
25 

25 
32 
32 
34 

35 
37 


12 
14 
15 
15 
1(> 

35 
36 


ILLUSTRATIONS. 

I.  Fig.  1. — Diurnal  variations  of  the  meteorological  elements  in 
the  atmosphere  at  the  surface  of  the  earth 

2. — Diurnal  variations  of  the  meteorological,  electrical, 
and  magnetic  elements  in  the  atmosphere  at 
some  distance  above  the  ground  

3. — Energy  spectra  at  solar  temperatures  reduced  to  the 
distance  of  the  earth 

4. — Energy  spectra  at  terrestrial  temperatures 

5. — Illustrating  the  formation  of  the  double  and  single 
diurnal  periods  of  the  absolute  humidity  

II.  Fig.  1. — Comparison  of  the  total  sun-spot  area,  1854-1891,  with 
the  magnetic  curves  in  the  26.68-day  period. . . . 

2. — Observed  variation  of  the  relative  frequency  of  the 
solar  prominences  in  10-degree  zones 

3. — Mean  variation  in  the  distribution  in  latitude  during 
the  11-year  periods  of  the  interval  1872-1900  .  . . 

4. — Movement  of  the  maximum  point  of  relative  fre- 
quency in  latitude  during  an  11-year  cycle  of 
the  solar  prominences,  spots,  and  faculte  

III.  Chart    1.— Sea  level  (January  2,  1903) 

2.— 3500-foot  level  (January  2,  1903) '. 

3.— 10,000-foot  level  (January  2,  1903) 

4. — Sea-level  components,  (January  2,  1903) 

5. — 3500-foot  level  components,  (January  2,  1903)  .... 

6.— 10,000-foot  level  components,  (January  2,  1903)     . 

7.— Sea  level  (January  7,  1903) 

8.— 3500-foot  level  (January  7,  1903) 

9.— 10,000-foot  level  (January  7,  1903) 

10. — Sea-level  components,  (January  7,  1903)  

11. — 3500-foot  level  components,  (January  7,  1903)  .... 
12.— 10,000-foot  level  components,  (January  7,  1903)  .  . 

IV.  Chart  13.— Sea  level  (February  7,  1903) 

14.— 3500-foot  level  (January  7,  1903) 

15.— 10,000-foot  level  (February  7,  1903) 

16.— Sea  level  (February  8,  1903) 

17.— 3500-foot  level  (February  8,  1903) 

18.— 10,000-foot  level  (February  8,  1903) 

19.— Sea  level  (February  27,  1003) 

20.— 3500-foot  level  (February  27,  1903) 

21.— 10,000-foot  level  (February  27,  1903) 

22.— Sea-level  components,  (February  27,  1903) 

23.— 3500-foot  level  components,  (February  27,  1903)  .  . 

24.— 10,000-foot  level  components,  (February  27,  1903). 

Fig.     25. — The  formation  of  local  anticyclones  and  cyclones 

in  the  general  circulation  about  the  poles 

26. — The  vectors  of  motion  and  their  components  in 
anticyclones  and  cyclones  at  the  1000-mile  and 
3000-mile  levels  

27. — The  stream  lines  at  cumulus  levels  for  cyclones 
and  at  cirrus  levels  for  hurricanes 

28. — Scheme  of  the  distribution  of  the  eastward  drift 
by  the  penetration  of  a  cyclono  vortex  into  the 

upper  strata  

IU 


10 


13 


17 

20 
20 
20 
21 
21 
21 
22 
22 
22 
23 
23 
23 

26 
26 
26 
27 

27 
27 
28 
28 
28 
29 
29 
29 

31 


33 
33 


ERRATA. 

Page  33,  column  1,  description. of  fig.  26,  for  "  miles  "  read  "meter  "  in  both  cases.     Page  33,  fig.  27,  column  2,  transpose 
the  legends  of  figs.  I  and  II,  but  not  the  numbers, 
iv 


STUDIES  ON  THE  METEOROLOGICAL  EFFECTS  OF  THE  SOLAR  AND  TERRESTRIAL 

PHYSICAL  PROCESSES. 


I.— THE  SEMIDIURNAL  PERIODS  IN  THE  EARTH'S  ATMOSPHERE. 


THE    DOUBLE    AND    THE    SINGLE    DIURNAL    PERIODS. 

The  problem  of  accounting  for  the  well  known  semidiurnal 
periods  in  the  meteorological  elements,  barometric  pressure, 
vapor  tension  or  humidity,  and  electric  potential,  as  observed 
at  the  surface  of  the  earth,  is  still  awaiting  its  complete  solu- 
tion, but  since  additional  information  on  the  subject  has  been 
obtained  in  the  past  few  years  through  the  different  kinds  of 
observations  in  the  strata  at  higher  levels  above  the  ground, 
this  is  sufficient  reason  for  bringing  the  subject  before  this 
section1  of  the  American  Association  for  the  Advancement  of 
Science.  Fig.  1  shows  the  average  curves  deduced  from  the 
surface  observations,  as  they  have  been  repeatedly  made  in 
all  parts  of  the  tropical  and  temperate  zones.2 

There  are  two  minima  and  two  maxima,  the  first  minimum  at 
about  4  a.  m.,  the  second  at  about  4  p.  m. ;  the  first  maximum 
at  about  10  a.  m.,  and  the  second  at  8  to  10  p.  in.  If  the  sun 
is  supposed  to  rise  and  set  at  6  o'clock,  this  indicates  that  the 
diurnal  atmospheric  processes  lag  several  hours  behind  the 
hour  angle  of  the  sun,  just  as  the  seasonal  processes  lag  about 
forty  or  fifty  days  behind  the  annual  temperature  changes. 
Since  this  retardation  occurs  chiefly  through  the  slow  radiation 
and  convection  of  the  atmosphere,  just  as  the  annual  tempera- 
ture wave  lags  in  penetrating  the  ground  through  its  slow  con- 
duction, so  therefore,  these  retardations  in  the  diurnal  elements 
may  become  the  means  of  calculating  the  coefficients  of  con- 
ductivity and  convection  in  the  air.  Now  it  is  to  be  noted  that 
while  the  pressure,  vapor  tension,  and  electric  potential  give 
a  decided  double  period,  the  diurnal  actinic  radiation  from  the 
sun  shows  only  a  small  midday  depression,  and  the  temperature 
none  at  all,  for  this  is  a  curve  with  a  single  maximum  at  3  p.  m. 
and  a  minimum  at  4  a.  m.  This  suggests  the  problem  to  be 
resolved,  namely,  the  occurrence  of  single  and  double  diurnal 
periods  at  the  same  time  in  the  lower  strata  of  the  atmosphere. 

In  past  years,  before  it  was  recognized  that  the  single  period 
prevails  throughout  the  atmosphere,  except  in  its  lowest  layers, 
efforts  were  made  to  account  for  the  surface  double  period 
in  two  ways  :  (1)  by  referring  it  to  a  dynamic  forced  wave 
involving  the  entire  atmosphere,  as  was  done  by  Lord  Kelvin, 
and  (2)  by  seeking  to  explore  the  possible  connections  between 
the  observed  waves  and  the  manometric  waves  due  to  temper- 
ature effects  in  the  lower  strata.  The  first  of  these  theories 
must  be  abandoned  for  weighty  reasons:  (1)  because  the  double 
wave  does  not  exist  throughout  the  atmosphere,  as  has  been 
stated,  but  is  confined  to  the  lowest  strata;  (2)  because 
the  double  wave  system  breaks  at  the  latitudes  CO0  north 
and  south,  and  reappears  in  the  polar  zones  at  right  angles  to 
that  system,3  with  a  change  in  the  phase  of  90° ;  and  (8)  because 
there  is  no  known  physical  principle  requiring  the  existence 

1  Road  before  the  Physics  Section,  B,  of  the  American  Association  for 
the  Advancement  of  Science  at  the  Washington,  D.  C. ,  meeting,  Decem- 
ber 28,  l'M'2. 

2  Compare  pages  120  and  121  of  my  paper,  Eclipse  Meteorology  and  Allied 
Problems,  Weather  Bureau  Bulletin  I,  1902. 

3  International  Cloud  Report,  chapter  9. 


of  any  semidiurnal  forced  wave  system.  The  second  theory  is 
not  satisfactory  because  it  has  been  found  impossible  to  estab- 
lish any  positive  synchronism  in  its  details  between  the  tem- 
perature changes  and  the  corresponding  diurnal  variations 
of  pressure  due  to  manometric  heat  effects.  Dr.  Julius  Hann  for 
years  sought  to  explain  the  phenomena  along  these  lines,  but 
was  obliged  to  abandon  the  attempt  and  to  accept  Lord  Kelvin's 
dynamic  wave  theory  for  want  of  anything  better  at  hand. 


FIG.  1. — Diurnal  variations  of  the  meteorological  elements  in  the  at- 
mosphere at  the  surface  of  the  earth. 

Like  so  many  other  scientific  problems  which  are  difficult  of 
solution,  the  trouble  apparently  lies  in  the  fact  that  the  neces- 
sary observations  have  not  been  made  in  the  right  place.  It 
was  supposed  that  the  variations  noted  at  the  ground  were 
common  to  the  adjacent  strata  up  to  considerable  heights,  but 
since  meteorologists  have  succeeded  in  getting  some  upper 


air  observations,  this  supposition  turns  out  to  be  contrary  to 
fact,  as  is  indicated  by  tig.  2. 

Figure  2  is  based  on  data  that  are  now  easily  accessible, 
and  we  need  not  quote  the  authorities  in  detail.  Generally 
speaking,  when  we  go  upward  from  the  surface  of  the  ground 
into  the  atmosphere,  all  the  double  diurnal  periods  become 
single  periods,  and  this  occurs  at  a  comparatively  low  elevation. 
Thus  at  the  top  of  the  Eifel  Tower  the  double  periods  greatly 


Mid  12,  1456789 


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FIG.  2.— Diurnal  variations  of  the  meteorological,  electrical,  and  mag- 
netic elements  in  the  atmosphere  at  some  distance  above  the  ground. 

weaken  or  entirely  disappear,  and  at  the  elevation  of  one  or 
two  miles,  where  the  convectional  ascents  of  the  aqueous  vapor 
contents  of  the  air  cease  to  form  cumulus  clouds,  only  the 
single  period  seems  to  exist.  Thus  the  truncated  actinometer 
curve  with  serrated  top,  fig.  1,  becomes  the  parabolic  curve, 
fig.  2,  even  at  the  surface  when  observed  in  very  dry  atmos- 
phere ;  the  barometric  pressure  curve  and  the  vapor  tension  or 
the  absolute  humidity  curves  synchronize  with  the  surface 


temperature  curve,  which  itself  retains  the  single  period  as  high 
up  as  any  diurnal  variations  occur,  and  the  electric  potential 
fall  becomes  a  single  period  curve  at  surprisingly  short  dis- 
tances above  the  surface.  Finally,  in  the  temperate  zones  the 
diurnal  wind  components,  and  the  magnetic  deflecting  vectors 
of  the  earth's  magnetic  field,  not  only  agree  together  as  vectors 
constituting  a  single  system,  but  they  also  synchronize  in  their 
turning  points  and  phases  with  all  the  other  elements  just 
mentioned.  It  is  impracticable  to  go  through  a  full  descrip- 
tion of  the  local  exceptions  to  the  general  conditions,  but  they 
form  a  most  interesting  study  for-the  meteorologist  who  keeps 
in  mind  their  significance  in  connection  with  the  great  cos- 
iiiicnl  problems  in  physics.  Enough  has  been  said  to  show 
that  we  need  to  fix  our  attention  upon  the  cause  of  the  trans- 
formation of  the  double  period  into  the  single  period  in  the 
lowest  strata  of  the  atmosphere. 

77ie  solar  radiation. — -In  my  judgment  there  can  be  but  one 
line  of  argument  that  needs  to  be  discussed,  namely,  the  be- 
havior of  the  aqueous  vapor  in  the  presence  of  the  solar  and 
the  terrestrial  radiations.  The  water  content  of  the  atmos- 
phere at  any  elevation  is  determined  by  the  temperature  and 
humidity  of  the  air,  and  therefore  the  unit  volumes  contain- 
ing equal  vapor  contents  stand  upon  isothermal  surfaces  which 
span  the  Tropics  in  great  arches,  stretching  from  the  north 
polar  zone  to  the  south  polar  zone.  These  vapor  contents 
rise  daily  from  lower  to  higher  levels  during  the  forenoon 
and  midday,  but  sink  back  again  during,  the  afternoon  and 
evening  hours.  The  process  is  well  understood  and  it  is 
briefly  as  follows:  The  incoming  solar  radiation  of  short  waves 
penetrates  the  earth's  atmosphere,  with  depletion  of  the  short 
waves  by  selective  reflection,  and  of  the  long  waves  by  the 
absorption  in  the  aqueous  vapor;  the  earth's  surface  is  heated 
by  the  residue  of  the  radiation,  and  it  then  radiates  like  a 
black  body  at  its  own  temperature,  which  being  relatively  low 
limits  the  outward  radiation  to  much  longer  terrestrial  waves 
than  the  incoming  solar  rays.  The  heat  received  at  the  surface 
also  evaporates  the  water  of  the  surface,  heats  the  lower 
strata,  and  raises  the  isotherms  by  convection  currents  as  well 
as  by  radiation,  till  at  the  average  elevation  of  1000  to  2000 
meters  the  vapor  tends  to  condense  or  actually  forms  the  visi- 
ble clouds.  The  outgoing  radiation  is  also  depleted  by  aque- 
ous vapor  absorption,  and  this  with  greatly  increased  vigor 
at  the  level  where  the  water  vapor  turns  into  liquid  water  in 
the  first  stage  of  condensation.  We  have,  therefore,  a  daily 
rise  and  fall  of  the  vapor  in  the  lower  atmosphere,  and  it  is 
the  behavior  of  this  vapor  blanket  which  must  be  studied 
carefully  to  account  for  the  transformation  of  the  double  daily 
into  the  single  daily  periods  described  above.  But  it  will  be 
desirable  to  examine  a  little  more  fully  the  peculiarities  of  the 
solar  and  the  terrestrial  radiations  before  going  on  to  our 
conclusions. 

Let  J  =  the  radiation  from  any  single  spectral  line  of  a  black 
body. 

<7m  =  the  maximum  radiation  occurring  in  the  spectrum  of  a 
black  body. 

Ja  =  the  total  radiation  throughout  the  whole  spectrum  from 
a  unit  surface  of  a  black  body. 

/i    =  the  wave  length  corresponding  with  •/. 

/m  =  the  maximum  wave  length  corresponding  with  .7"m. 

Tj  =  the  absolute  temperature  of  the  emitting  body. 

Tj  =  the  absolute  temperature  of  the  absorbing  body. 

A  =  the  solar  constant  or  the  value  of  J"o  at  the  distance  of 
the  earth  from  the  sun. 

R  =  the  Tadius  of  the  sun  in  kilometers. 

d  =  the  distance  of  the  earth  from  the  sun  in  kilometers. 

Then  we  obtain  by  the  Wien-Paschen  formulas  in  units  of 
gram  calories  per  on2  per  second,  per  minute,  and  per  day, 
respectively,  the  following  equations: 


Radiation  function  in  the  normal  xprctrum. 

I.  Radiation  from  a  single  spectral    line  in    gram  calories 
per  cm1. 


9.292  x  10s      Gr.  Cal. 

Logarithms. 

0.96811 
5.74626 
8.90462 
4.16002 
3.79780 

a  iflfiiQ     20 

/      «2TM\  cm2,  second. 

#uo  "2  ) 

1.277xlO-12c24      1.277  x  1Q-12  (14455)4 

1  ~               6                                    6 
=  9.292  x  10s  per  sec. 
=  5.575  x  IO5  per  min. 
=  8.028  x  IO8  per  day. 
c,  =  5  x  2891  =  14455 
cW=  14455  x  0.43429=  6277.4 
II.  Total  radiation  of  a  black  body. 

1    O77       sx   1  H—  12  /  7'<          T4\           '       '         i-vciv  oof» 

=  7.6G2    x  10-U(T,4—  r/)        "        per  miu. 
=  1.1033  x  IO-1  (T,4—  TJ)        "        per  day. 

9.88434—20 
13.04270—20 

The  solar  constant  A  =  .T  x 


IF 

<r 


=  J  x  2.1643  x  IO-5  per  min.       5.33532—10 
Radius  of  the  sun.  R  =  695  500 kilometers.  5.84230 

Distance  of  earth  from  sun.  d  =  149  500  000  kilos.      8.17464 
.      A  =  7.662    x  10-"  ( r,4  —  ?;4)  x  2.1643  x  10"5 
=  1.6583  x  10-15(r,*—  T*)  per  miu. 

III.  Maximum  radiation  in  a  normal  spectrum. 
P;  ^7^  v  in5  v  f^5 

o.CWt)  X  1  )    X  o 

(14455)5 102-17145 
=  3.1004  x  IO-16  T5  per  sec. 
=  1.8602  x  10-"  T*  per  min. 
=  2.6787  x  10~n  T5  per  day. 
.7        3.1004  x  IO-16  T 

IV-  /  =  orriTKFB  7<4  =  2-4289x 

V.  ;  ^=2891. 


J  = 


io5-" 


J-        


5.21966—20 


4.49141—20 
6.26956—20 
9.42792—20 


T. 


6.38522—10 
3.46105 


Meteorology.  At  all  these  temperatures  the  ratio  <7m/  J0  seems 
to  be  normal,  but  at  the  higher  solar  temperatures  this  is  no 
longer  the  case.  It  may  therefore  be  the  fact  that  the  extra- 
polation to  such  temperatures  as  T=  7000°  to  8000°  is  not  al- 
lowable without  a  considerable  change  in  these  constants,  or 
even  in  the  exponents  of  the  formula.  It  may  be  that  there  is 
a  breakdown  in  the  molecular  structures  of  so-called  black 
bodies  at  very  high  temperatures,  which  causes  them  to  emit 
quite  different  spectra  curves  from  those  which  we  have  com- 
puted by  these  formulae.  If  this  point  of  view  is  correct,  it 
will  be  necessary  to  move  very  cautiously  in  computing  the 
value  of  the  solar  constant,  at  the  distance  of  the  earth,  from 
formulae  deduced  in  our  laboratories  and  applied  to  the  sun 
as  to  a  common  black  body. 

By  means  of  these  formulae  we  construct  the  solar  and  ter- 
restrial curves  for  various  temperatures  for  the  incoming 
radiation  of  the  sun,  supposing  it  to  range  from  8000°  to 
3000°;  also  for  the  outgoing  radiation  from  the  earth  with  a 
range  of  from  383°  to  198°  absolute  temperature.  The  cor- 
responding coordinates  are  given  in  Tables  1  and  2;  they  are 
also  plotted  graphically  on  fig.  3  for  the  sun,  and  on  fig.  4 
for  the  earth.  On  the  solar  curve  for  T=  6000°  is  placed 
Professor  Langley's  energy  curve  as  derived  by  the  bolometer 
observations. 

TABLE  1. — Energy  spectra  at  solar  temperatures  reduced  to  the  distance  of 
the  earth,  expressed  in  units  of  gram  calories  per  square  centimeter  per 
minute. 


(Eclipse  Meteorology  and  Allied  Problems,  page  164.) 
From  formula  IV  we  have  the  following  equation: 

Jm  =  0.00024  T  x  Ja. 
Hence,  for 

T=      100°;  J  =  0.024  J ;  and  J  =  42       Jm. 
T=    1000°;  /'  =  0.24    /;  J=    4.2    J  . 

T=  10000° ;  J°  =  2.4      J ;  J0  =    0.42  Jm. 

That  is  to  say  for  low  temperatures  the  total  radiation  Ja  is 
much  greater  than  the  maximum  radiation  Jm,  but  for  high 
temperatures  .7o  becomes  less  than  Jm.  Since  Jo  is  the  integral 
of  the  area  of  the  curve  of  energy  intensity,  it  should  evidently 
be  greater  than  Jm  under  all  circumstances,  but  the  fact  that 
by  this  formulae  (IV)  it  becomes  less  for  temperatures  above 
4119°  seems  to  indicate  that  there  may  be  something  wrong 
in  the  deduction  of  the  formulae  III  for  Jm  and  II  for  Jo,  from 


which  IV  for  '-^  was  derived. 


These  formulae  and  constants 


have  been  tested  by  mirnerous  experiments,  and  they  appear 
to  be  satisfactory  for  temperatures  up  to  about  T=  1500°.  It 
is  noted  that  there  is  a  tendency  for  the  coefficients  r,,  r2  to 
change  in  passing  from  low  temperatures  and  long  wave 
lengths  (T=  273°  to  750°)  to  higher  temperatures  and  longer 
wave  lengths  (T=  750°  to  1500°).  Compare  page  164,  Eclipse 


T. 

8,000° 

7,000° 

6,000° 

5,000° 

4,000° 

3,000° 

A  =0.0,i 

0.00 

0.1  . 

0.02 

0.00 

0.00 

0.2. 

4.50 

1.24 

0.22 

0.02 

5.  575  X  IO5 

0.3. 
0.4. 
0.5. 

12.  03 
12.87 
10.41 

5.09 
6.75 
6.21 

1.62 
2.85 
3.12 

0.32 
0.86 
1.19 

0.03 
0.14 
0.28 

0.01 
0.03 

f       6277.  4  \ 

A  10^'-  ) 

0.6. 

7.64 

4.96 

2.80 

1.25 

0.38 

0.05 

0.7. 

5.43 

3.76 

2.30 

1.15 

0.40 

0.07 

Gr.  Cal. 

0.8. 

3.85 

2.79 

1.81 

0.99 

0.40 

0.09 

Jm  units  mS  mlnute; 

0.9. 

2.81 

2.  06 

1.41 

0.82 

0.37 

0.10 

1.0. 

1.98 

1.53 

1.09 

0.67 

0.33 

0.10 

1.1  . 

1.45 

1.15 

0.84 

0.54 

0.28 

0.09 

1.2. 

1.08 

0.87 

0.65 

0.44 

0.24 

0.09 

1.3. 

0.81 

0.66 

0.51 

0.34 

0.20 

0.08 

.4. 

0.62 

0.52 

0.40 

0.28 

0.17 

0.07 

.5. 

0.48 

0.40 

0.32 

0.23 

0.14 

0.06 

.6. 

0.39 

0.32 

0.26 

0.19 

0.12 

0.06 

.7. 

0.30 

0.25 

0.21 

0.16 

0.10 

0.05 

.8. 

0.23 

0.20 

0.17 

0.13 

0.09 

0.04 

.9. 

0.19 

0.16 

0.14 

0.11 

0.07 

0.04 

2.0. 

0.15 

0.13 

0.11 

0.09 

0.06 

0.03 

2.5. 

0.06 

0.05 

0.05 

0.04 

0.03 

0.02 

3.0. 

0.03 

0.03 

0.02 

0.02 

0.02 

0.01 

Jm" 

13.19 

6.77 

3.13 

1.26 

0.41 

0.10 

»... 

0.36,i 

0.4V 

0.48,1 

0.58,1 

0.72,1 

0.96,1 

A  .. 

6.79 

3.98 

2.15 

1.04 

0.43 

0.13 

TABLE  2. — Energy  spectra  at  terrestrial  temperatures,  expressed  in  units  of 
gram  calories  per  square  centimeter  per  minute. 


T. 

383° 

373° 

323° 

303° 

288° 

273° 

258° 

243° 

228° 

213° 

198° 

A=  2,1. 

0.000 

3.. 

.008 

.006 

.001 

4  .. 

.044 

.034 

.007 

.004 

.002 

.001 

6.. 

.134 

.113 

.041 

.  025 

.017 

.011 

.006 

.004 

.002 

.001 

.000 

8  .. 

.152 

.134 

.063 

.044 

.032 

.023 

.015 

.010 

.006 

.004 

.002 

10  .. 

.128 

.116 

.064 

.047 

.037 

.028 

.021 

.015 

.010 

.006 

.004 

12    . 

.097 

.089 

.055 

.042 

.034 

.027 

.021 

.016 

.012 

.008 

.005 

14  .. 

.070 

.065 

.042 

.034 

.028 

.024 

.019 

.015 

.011 

.008 

.006 

n;  .. 

.050 

.047 

.032 

.027 

.023 

.019 

.016 

.013 

.010 

.007 

.006 

18  .. 

.03li 

.034 

.025 

.021 

.018 

.016 

.013 

.011 

.009 

.007 

.005 

20    . 

.027 

.025 

.019 

.016 

.014 

.(112 

.011 

.009 

.007 

.006 

.005 

22    . 

.019 

.018 

.014 

.012 

.011 

.010 

.0011 

.007 

.006 

.005 

.004 

24    . 

.015 

.014 

.011 

.010 

.009 

.008 

.007 

.006 

.005 

.004 

.003 

26    . 

.011 

.011 

.008 

.007 

.007 

.006 

.005 

.005 

.004 

.003 

.003 

28    . 

.008 

.008 

.007 

.006 

.005 

.005 

.004 

.004 

.003 

.003 

.002 

30    . 

.007 

.006 

.005 

.005 

.004 

.004 

.004 

.003 

.003 

.002 

.002 

32 

.006 

.005 

.004 

.004 

.004 

.003 

.003 

.003 

.  IKK! 

.002 

.002 

34 

.004 

.004 

.003 

.003 

.003 

.002 

.002 

.002 

.002 

.002 

.001 

•      36 

.003 

.003 

.003 

.003 

.003 

.002 

.002 

.002 

.002 

.001 

.001 

38 

.003 

.003 

.  002 

.002 

.002 

.001 

.001 

.001 

.001 

.001 

.001 

40 

.002 

.002 

.002 

.002 

.002 

.001 

.001 

.001 

.001 

.001 

.001 

J 

.153 

.134 

.065 

.048 

.037 

.028 

.021 

.016 

.011 

.008 

.006 

5: 

7.55,1 
1.649 

7.75»< 
1.483 

8.  95,i 
0.834 

9.54,t 
(I.  64(1 

10.  Oji 
o.  .-127 

10.  6,1 
0.  426 

11.2,, 
0.340 

11.9,i 
II.  2C.7 

12.  7n 
0.207 

13.  6n 
0.158 

14.  CM 
0.118 

Remarks  on  the  solar  constant. — This  exhibit  suggests  some 


0.0         OJp       0.8^      0.3ft.       0.4f4.     0.5^      0.6^.      0.7^.      0.8^.     0.9^      J.O^    J.JLL 


/.Sij.      l.'Ju.       l.Su.      J.6ju      }.7u-      J£u.     J.StJ.      V.Oi 


0.1  U.Z         0.3         04          as          0.6         0.7          0.9         0.9         1.0         J.J 


1.3          J.t         1.S         J.6          1.7          l.Q         1.9         2.O 


FIG.  3.— Energy  spectra  at  solar  temperatures  reduced  to  the  distance  of  the  earth. 


6     8     JO     12     J4    JS     J8     20     2S    24    26     29    3O    32    34 


FIG.  4. — Energy  spectra  at  terrestrial  temperatures. 


comments  on  the  depletion  of  the  short  waves  by  selective  re- 
flection or  scattering,  and  of  the  long  waves  through  absorption 
by  aqueous  vapor.  According  to  F.  W.  Very's  discussions,* 
the  selective  depletion  and  absorption  in  the  solar  atmosphere 
of  the  radiation  from  the  photosphere,  may  be  due  to  four 
cooperating  causes:  (1)  to  a  considerable  extension  of  finely 
divided  solar  material  in  the  outer  corona  to  the  distance  of 
about  one  radius;  (2)  to  scattering  upon  the  molecules  and 
other  very  fine  particles  especially  in  the  inner  corona;  (3)  to 
the  passage  through  a  columnar  structure  having  different 
coefficients  of  transmission;  (4)  to  emission  from  the  uneven 
granular  surface  of  the  photosphere  radiating  at  different  tem- 
peratures. According  to  Professor  Schuster's  recent  paper,5 
the  depletion  effect  can  be  suitably  explained  by  "  placing  the 
absorbing  layer  sufficiently  near  the  photosphere  and  taking 
account  of  the  radiation  which  this  layer,  owing  to  its  high 
temperature,  must  itself  emit."  It  is  not  proper  to  regard 
the  radiating  photosphere  as  of  a  single  temperature,  but  as 
ranging  somewhat,  though  not  through  many  hundred  degrees, 
with  the  depth  of  the  strata,  the  lower  being  hotter ;  the  co- 
efficients of  transmission  vary  with  the  wave  length,  and  with 
the  extent  of  path  traversed,  and  therefore  with  the  marginal 
distance  of  the  ray  from  the  center  of  the  sun,  the  marginal 
transmission  being  rendered  more  efficient  by  early  sifting  out  of 
the  rays  that  are  easily  absorbed  by  the  existing  material.  In 
the  present  stage  of  the  problem  it  is  difficult  to  assign  the  exact 
percentage  of  absorption  due  to  the  sun's  atmosphere  taken  as  a 
whole,  and,  from  similar  considerations,  the  percentage  due  to 
the  absorption  in  the  earth's  atmosphere  remains  in  doubt. 
Hence,  it  is  not  easy  to  derive  the  true  temperature  of  the  sun's 
radiating  surface,  even  taken  as  an  integral.  Comparing  the 
Langley  curve  with  the  energy  curve  for  6000°,  it  suggests  that 
the  short  wave  ordinates  imply  a  temperature  of  about  5000°, 
but  that  the  long  waves  at  the  same  time  require  a  temperature 
of  rather  more  than  7000°,  especially  as  indicated  by  those  from 
1.5/i  to  1.7/i.  Dr.  Niles  Ekholm6  attempts  to  reconcile  these 
conflicting  facts  by  assigning  a  system  of  varying  tempera- 
tures, T=  5226  -f  lOOOA,  increasing  with  the  wave  length,  till 
T  equals  7226°  for  I  =  2.0.«.  While  this  brings  the  two  curves 
nearer  together  throughout  their  extent  there  are  two  diffi- 
culties yet  to  be  overcome:  (1)  the  sun's  atmosphere  depletes 
short  waves  most  in  its  lower  strata,  while  the  long  waves 
escape  more  readily,  some  of  them  apparently  quite  unaffected. 
Since  the  short  waves  by  Ekholm's  hypothesis  are  assigned  to 
lower  temperatures,  this  implies  that  they  are  emitted  only  by 
the  higher  strata  in  the  sun's  atmosphere,  and  therefore  it  fol- 
lows that  they  do  not  register  the  temperature  of  the  photo- 
sphere at  all  accurately.  Furthermore,  the  temperature  in 
the  solar  atmosphere  above  the  photosphere  can  not  have  a 
range  of  2000°.  (2)  If  the  long  waves  which  actually  pass 
through  both  the  atmospheres  of  the  sun  and  the  earth  do 
possess  energy  ordinates  corresponding  to  temperatures  as 
as  high  as  7200°  to  7500°  they  could  not  have  been  generated 
at  all  except  at  such  high  temperatures  as  these,  and  they  in 
fact  become  an  important  index  for  determining  the  efficient 
photospheric  temperature.  It  seems  to  me  that  since  the  long 
wave  radiation  at  1.5/i  to  1.7/i  requires  a  temperature  of  nearly 
7500°  we  must  let  this  fact  control  our  conclusions,  rather 
than  depend  upon  the  deductions  to  be  derived  from  estimated 
percentage  depletions  of  the  short  waves  of  the  spectrum.  It 
is  noted  that  this  gives  a  result  nearly  in  harmony  with  the  tem- 
perature T=  7535°,  which  was  assigned  by  me  to  the  photo- 

4  Atmospheric  Radiation,  F.  W.  Very,  Bulletin  G,  Weather  Bureau,  1900. 
The  solar  constant,  F.  W.  Very,  Monthly  Weather  Review,  August,  1901. 
The  absorption  power  of  the  solar  atmosphere,  F.  W.  Very,  Astro- 
physics, September,  190?. 

6  The  solar  atmosphere,  Arthur  Schuster,  Astrophysics,  January,  1903. 

6Ueber  Emission  und  Absorption  der  Warine  und  deren  Bedeutung  fur 
die  Temperatur  der  Erdoberflfiche,  Meteorologische  Zeitschrift,  January, 
1902. 


sphere  from  meteorological  considerations  (Eclipse  Meteoro- 
logy, page  SI).  Thus,  in  determining  the  hydrogen  gas  con- 
stant at  the  sun,  we  have, 

p  10333  (earth)  2851£5(fran) 

Ji  =  /'Jl\~  0.08!)!MM>  x  273°  =  O.OSDIMH!  x  7535°  * 
Since  ji  (sun)  =  10333  x  27.fi  =  285185,  it  follows  that 
273°  x  27.0  =  7535°,  is  the  absolute  temperature  of  the  photo- 
sphere. 

It-  was  found  that  the  rate  of  change  of  temperature  from 
the  photosphere  vertically  outward  seems  to  be  rather  small, 

-,.  =  —  0.013°  per  1000  meters,  that  is,  about  300°  from  the 

the  photosphere  to  the  top  of  the  inner  corona,  and  this  would 
indicate  that  we  do  not  have  in  the  sun's  upper  atmosphere 
such  extremes  of  temperature  to  deal  with  as  Ekholm's  formula 
requires.  But  if  we  assign  so  high  a  temperature  as  7535 
to  the  photosphere,  the  depletion  by  scattering  as  shown  by  the 
diagrams  of  fig.  3  must  be  much  greater  than  usually  assigned, 
as  is  evident  by  comparing  the  curves,  and  we  must  also  infer 
that  the  solar  constant  is  really  large  in  order  to  correspond 
to  this  temperature,  namely,  about  4.0  gram  calories  per 
square  centimeter  per  minute  at  the  outer  limits  of  the  earth's 
atmosphere. 

In  the  earth's  atmosphere  selective  scattering  takes  place 
on  the  molecules  of  the  constituents  of  the  air,  especially  in 
the  lower  strata,  and  absorption  occurs  throughout  the  shell 
occupied  by  the  aqueous  vapor,  but  also  chiefly  in  the  lower 
strata.  It  is  again  difficult  to  assign  the  relative  parts  due  to 
scattering  and  absorption,  respectively.  Prof.  F.  W.  Very 
contends  that  the  aqueous  vapor  of  the  higher  strata  first 
attacks  the  incoming  radiation  and  depletes  it  very  consider- 
ably and  thus  raises  the  temperatures  of  the  high  strata.  Our 
international  cloud  observations,  and  the  direct  temperature 
readings  in  balloon  ascensions  seem  to  sustain  this  view.  But 
Ekholm  argues  from  the  heat  content  of  the  atmosphere,  as- 
suming the  solar  constant  of  3.0  calories,  as  follows: 


Solar  constant  =  3.0  calories  per  minute . 

40  per  cent  absorbed  =  0.40  x  3.0 

Inward. — (1).  The  air  receives  one-fourth  of  this 


and  holds  it. 


432 
1440 


(2).  Conduction  to  be  neglected  .... 

(3).  Convection  to  be  neglected  .... 

Outward.—  (4).  From  vaporization  of  aqueous  va- 


3.00 
1.  20 


:   0.    30 

0.00 
0.  00 


por 


1G4 
1440 


=  0.  11 


(5).  Radiation    from    earth  =  50    per 

cent,  where  the  surface  receives    ,-.„ 

i  of  3.00  =  1.00 '    =  0.  07 

1440 


Total  received  per  minute 


694  =  0.  48 
1440 


This  corresponds  to  a  mean  temperature  of  the  air  8.6°  C., 
while  the  observed  mean  temperature  is  —  17.0°  C.,  or  too  low  by 
25.6°  C.  Ekholm  says:  "  It  follows  that  the  supposed  great  ab- 
sorption of  heat  by  the  atmosphere  does  not  take  place.  But 
we  must  admit  that  the  atmosphere  absorbs  directly  only  a 
small  fraction  of  the  insolation,  and  that  it  is  chiefly  warmed 
indirectly  from  the  earth's  surface."  In  a  word,  the  aqueous 
bands  absorb  some  little  heat,  while  the  air  is  nearly  diather- 
manous  to  the  rest  of  the  energy  spectrum.  I  shall,  however, 
venture  to  raise  the  following  inquiry.  Ekholm  seems  to  have 
assigned  certain  percentages  for  absorption,  which  of  course 
are  in  the  nature  of  a  conjecture  so  long  as  the  solar  tempera- 
ture remains  in  doubt,  and  a  part  of  the  discrepancy  between 
the  mean  temperature  of  the  earth's  atmosphere  as  observed 


and  as  deduced  from  the  solar  constant,  may  be  explained  in 
that  way.  But,  furthermore,  he  seems  to  compute  the  total 
energy  received  011  the  basis  of  a  twenty-four  hour  radiation, 
and  to  have  made  no  allowance  for  the  fact  that  the  earth  re- 
ceives only  twelve  hours  of  sunshine.  The  solar  constant  per 
minute  when  applied  to  the  residual  temperature  of  the  atmos- 
phere should  have  this  fact  included,  but  I  am  not  able  to  de- 
cide from  Ekholm's  paper  whether  this  was  done  in  fixing  upon 
his  percentages.  I  infer,  in  any  event,  that  the  common  pro- 
cedure of  extrapolating  to  the  value  of  the  solar  constant  on 
the  outer  atmosphere  by  using  the  spectrum  throughout  its 
entire  length  assigns  too  much  weight  to  the  short  waves, 
which  certainly  suffer  severely  from  scattering,  and  that  on 
the  other  hand  the  few  long  undepleted  waves  1.5/j.  to  1.7/z 
which  are  neither  absorbed  nor  scattered,  form  the  proper  basis 
for  deducing  the  true  solar  constant.  Judging  from  these  data 
it  is  probably  not  far  from  4.0  calories,  and  the  temperature 
of  the  photosphere  must  be  about  7500°. 

The  terrestrial  radiation. — If  the  energy  line  plotted  on  curve 
T  =  288°  of  fig.  4  represents  the  observed  earth's  transmission 
through  the  air  as  described  by  Very  (see  Bulletin  G,  page 
124),  it  seems  to  be  in  conflict  with  the  view  that  the  earth 
radiates  like  a  black  body  of  low  temperature.  The  strong 
absorption  from  /  =  4  /i  to  8  rt  is  evidently  due  to  aqueous  vapor, 
but  the  much  greater  absorption  area  from  ).  =  12  rt  to  40 /x  is 
apparently  not  to  be  attributed  to  the  same  cause.  It  seems 
to  me  much  more  probable  that  the  earth  does  not  radiate 
these  long  waves  like  a  black  body,  but  is  really  deficient  in 
them  and  emits  freely  only  the  waves  from  /  =  4,u  to  12, a. 
On  the  other  hand  Ekholm7  has  drawn  the  curve  from  ll//  to 
20/j.  in  quite  a  different  manner,  by  extrapolating  from  Lang- 
ley's  corrected  observations  on  the  moon's  radiation,  so  as  to 
follow  the  normal  energy  curve  much  more  closely. 

Since  no  observations  exist  to  determine  this  point  it  may 
still  be  left  open  to  doubt  whether  the  waves  are  emitted  or  not. 
If  they  are  really  emitted,  then  the  air  must  have  other  ab- 
sorbing constituents  that  have  not  yet  been  attributed  to  it  to 
satisfy  Very's  curve. 

We  may  now  study  briefly  the  effect  of  the  earth's  long- 
wave radiation  upon  the  meteorological  elements,  and  explain 
the  occurrence  of  the  double  periods  at  the  surface  and  single 
periods  at  the  cumulus  cloud  levels.  If  the  scattering  effect 
throws  back  into  space  a  considerable  percentage  of  the  in- 
coming radiation  so  that  it  does  not  reach  the  earth  at  all,  on 
the  other  hand  the  absorption  by  the  aqueous  vapor  of  the 
terrestrial  long  waves  tends  to  efficiently  conserve  the  earth's 
temperatures  which  are  high  relatively  to  that  of  the  inter- 
planetary space,  and  at  the  same  time  it  generates  a  series  of 
interesting  physical  processes  which  can  be  described  with  at 
least  approximate  correctness.  A  field  of  research  of  unusual 
importance  and  interest  is  here  presented  to  the  meteorolo- 
gist. The  discussion  of  the  temperature  and  vapor  pressure 
observations  which  have  been  taken  in  the  United  States, 
during  the  past  thirty  years,  is  now  going  on  at  the  Weather 
Bureau,  and  we  hope  to  be  able  to  make  some  further  contribu- 
tions to  this  subject  by  extending  to  the  further  study  of  the 
cloud  formations  those  therinodynamic  processes  which  were 
applied  in  a  few  cases  in  the  International  Cloud  Report. 

We  adopt  the  hypothesis  that  aside  from  a  moderate  ab- 
sorption of  solar  radiation  by  the  aqueous  vapor  in  the  atmos- 
phere, the  waves  pass  through  it  unimpeded,  except  by  scat- 
tering, which  turns  back  a  considerable  percentage  into  space. 
The  energy  of  the  portion  reaching  the  earth's  surface  is  ex- 
pended in  raising  its  surface  temperature.  This  increases 
from  early  morning  till  midday,  with  a  lag  of  about  two  hours 
due  to  the  slowness  of  propagation  of  the  physical  effects  into 

7  Ueber  Emission  und  Absorption  der  Warrae  und  deren  Bedeutung  f  iir 
die  Temperatur  der  Erdoberflache.  Nils  Ekholm,  Mot.  Zeit.,  November, 
1902. 


the  atmosphere,  and  then  declines  in  the  reverse  order  till 
midnight.  The  earth  radiates  in  the  forenoon  something  like 
a  black  body  of  gradually  increasing  temperature,  the  longest 
waves  being  possibly  excluded,  though  their  energy  has  not 
yet  been  mapped  out  beyond  I  =  12//..  The  aqueous  vapor  de- 
pletes the  outgoing  radiation  strongly  in  the  waves  4/t  to  8/i 
and  probably  from  12,u  to  20//.  It  is  especially  to  be  noted 
that  when  water  vapor  turns  to  liquid  water  in  cloud  conden- 
sation the  power  of  aqueous  absorption  is  increased  a  hundred 
fold,  and  thus  the  generation  of  clouds  forms  at  the  same  time 
an  absorbing  screen  at  the  cumulus  level  which  practically 
confines  the  radiation  emanating  from  the  land  and  the  ocean 
to  the  strata  within  a  mile  or  two  above  the  earth's  surface. 
Carbon  dioxide,  CO,,  can  absorb  only  its  own  peculiar  rays, 
and  as  these  constitute  only  a  small  portion  of  the  spectrum 
their  total  effect  is  small  compared  with  that  of  the  aqueous 
vapor. 

Explanation  of  the  formation  of  the  two  types  of  diurnal  periods. — 
Let  us  illustrate  the  formation  of  the  double  diurnal  period  at 
the  earth's  surface  and  the  single  period  in  the  cumulus  level 
by  considering  the  behavior  of  the  absolute  humidity,  that  is 
the  number  of  grams  of  water  vapor  per  cubic  centimeter. 
The  first  diurnal  effect  of  the  radiation  from  the  earth  is  to 
raise  the  vapor  content  of  the  atmosphere  from  the  low  level 
occupied  by  it  at  night  to  a  higher  level  during  midday.  This 
absorbing  screen  of  water  vapor,  visible  or  not,  rises  and  falls 
once  daily  through  1000  or  2000  meters,  taken  as  a  whole. 
While  the  warm  air  rises  by  convection  from  the  surface  to 
the  level  of  1500  meters,  the  vapor  rises  with  it  and  endeavors 
to  saturate  the  unit  volumes  of  the  higher  strata  at  the  pre- 
vailing lower  temperatures,  the  depleted  lower  volumes  being 
partially  filled  up  again  by  fresh  evaporation  from  the  water  and 
land  surfaces.  Thus,  in  fig.  5,  which  represents  the  humidity 


.Diurnal Absolute  Humidify 
in  tke  Cumulus  CXoual Level. 

Mte&t. 


7p.m. 


^Midn. 


Capacity -/or  vapor 
contents  per  ettttt 
volume  with  change 
of  tem 


JDiurnal 'Te 


FIG.  5. — Illustrating  the   formation  of  the   double   and   single   diurnal 
periods  of  the  absolute  humidity. 

variations  at  the  earth's  surface  and  at  the  cumulus  level,  and 
the  temperature  changes  at  all  levels  up  to  a  moderate  elevation 
of  probably  3000  or  4000  meters,  we  may  consider  the  be- 
havior of  the  successive  volume  capacities  arranged  in  vertical 
lines.  There  is  a  decrease  in  actual  temperature  with  the 
elevation,  and  therefore  the  saturated  unit-volume  content 
decreases.  The  vapor  sheet  rises  to  higher  levels,  and  this, 
together  with  the  fresh  supply  by  evaporation  from  the  sur- 
face, can  refill  the  depleted  volume  again,  especially  during 


8 


the  forenoon  hours.  After  the  noon  hour  the  continued  in- 
crease of  temperature  gives  rise  to  larger  vapor  capacity  per 
unit-volume,  represented  by  larger  areas  on  the  diagram  which 
are  shaded  more  thinly  and  decrease  upward  in  dimensions. 
But  while  the  rising  vapor  sheet  keeps  the  upper  volumes  filled, 
the  lower,  which  are  drained  by  the  ascension  of  the  \\ater 
vapor,  can  not  be  supplied  by  evaporation  at  the  surface  at  a 
sufficiently  rapid  rate  to  keep  them  full,  because  the  prevail- 
ing surface  moisture  has  been  taken  up  at  an  earlier  hour. 
The  same  remarks  are  true  for  the  relative  humidities.  The 
result  is  that  the  upper  volumes  are  always  full,  or  relatively 
full,  and  have  an  increasing  actual  content  up  to  the  early 
afternoon,  about  2  p.  in.,  so  that  the  diurnal  curve  at  some 
distance  above  the  ground  has  a  single  maximum  and  minimum 
as  observed.  On  the  other  hand,  while  the  10  a.  m.  surface 
volumes  are  kept  tilled,  or  relatively  tilled,  they  are  actually 
depleted  in  the  afternoon  and  are  not  replenished  by  evapora- 
tion up  to  the  original  relative  humidity  of  the  morning,  and 
therefore  the  curve  shows  a  depression  in  the  early  afternoon, 
and  is  doubly  periodic.  The  second  maximum  at  the  surface 
is  due  to  a  reversal  of  this  process  as  the  vapor  settles 
back  slowly  to  the  ground  during  the  afternoon  and  night. 
The  additional  lag  of  the  evening  maximum,  being  four  hours 
in  the  evening  to  about  10  p.  m.,  is  due  to  the  slow  cooling  of 
the  ground  after  sunset,  which  continues  to  be  a  source  of 
heat  for  several  hours,  and  the  slow  conductivity  of  the  heated 
atmosphere,  which  retains  its  heat  even  longer  than  the  ground 
after  the  sun  has  set.  This  theory,  if  pursued  into  quantita- 
tive details  will  evidently  account  for  the  entire  series  of  ob- 
served phenomena,  and  I  hope  to  continue  the  study  of  this 
subject  with  such  data  as  are  now  at  the  disposal  of  meteor- 
ologists. If  we  compare  the  areas  of  the  complete  actinometer 
curve  of  fig.  2  with  that  of  tig.  1,  as  it  is  observed,  the  trun- 
cated portion  must  represent  the  heat  energy  that  has  been 
converted  into  work  in  carrying  out  these  physical  processes. 
Like  an  engine  indicator-diagram,  the  difference  between  these 
curves  can  be  translated  as  a  function  of  the  process  concerned 
in  the  double  diurnal  periods  in  the  lower  strata,  and  thus 
become  an  important  means  of  studying  this  function  in  the 
free  atmosphere.  If  we  could  have  suitable  observations  of 
the  several  elements  at  all  levels  up  to  1  or  2  miles  high,  it 
would  be  a  comparatively  easy  problem  to  discuss  to  a  con- 
clusion. At  present  the  serious  difficulty  is  to  secure  the 
necessary  data  since  we  must  resort  to  more  or  less  indirect 
methods. 

The  remaining  elements  may  be  treated  for  the  change  of 
period  in  a  very  few  words.  Analyzing  the  diurnal  barometric 
pressure  by  volume  contents  we  see  that  with  the  heating  of 
the  lower  strata  the  denser  air  of  night  is  replaced  by  contents 
of  lower  density  after  midday;  taking  into  account  the  lag,  the 
lower  volumes  are  depleted  and  the  upper  are  filled  relatively, 
thus  producing  the  two  types  of  periods.  This  is  entirely 
analogous  to  the  barometric  pressures  of  winter  and  summer 
wherein  the  summer  pressures  are  lower  at  the  surface  of  the 
earth,  but  greater  at  some  such  level  as  1500  to  2000  meters, 
the  summer  pressure  corresponding  to  that  of  the  diurnal  pres- 
sure in  the  afternoon.  The  later  diurnal  lag  in  the  evening  to 
10  o'clock  is  a  function  of  the  cooling  of  the  lower  atmosphere 
by  convection  and  radiation,  and  the  settling  back  of  the  vapor 
sheet  to  the  surface  of  the  ground.  The  details  of  this  phe- 
nomenon, as  given  in  chapter  9  of  the  International  Cloud  Re- 
port, can  all  be  shown  to  be  in  accord  with  this  view,  especially 
since  the  efficient  vapor  action  caused  by  the  lifting  of  the  vapor 
sheet  through  radiation  occurs  outside  the  polar  zones,  and  is 
greatest  in  the  Tropics.  It  should  be  admitted  that  we  do  not 
yet  understand  the  cause  of  the  change  of  the  phase  of  the 
diurnal  barometric  pressure  which  takes  place  in  the  polar 
zones.  It  is  inferred  from  these  considerations  that  since  the 
double  diurnal  period  is  confined  to  a  thin  sheet  near  the  sur- 


face, and  does  not  extend  throughout  the  atmosphere,  Lord 
Kelvin's  theory  of  a  dynamic  forced  wave  is  not  available  for 
explaining  this  phenomenon.  Dr.  Harm's  difficulties  regarding 
the  synchronism  of  the  temperature  with  the  diurnal  barometric 
pressure  will  also  probably  disappear,  because  the  local  be- 
havior of  the  vapor  sheet  in  dry  and  moist  localities  will  impose 
strongly  modifying  conditions  upon  the  efficient  action  of  the 
surface  temperatures  in  respect  to  the  two  types  of  periods. 

The  fact  that  water  vapor  is  a  very  powerful  absorbent  of 
given  waves,  and  that  this  occurs  chiefly  in  the  cumulus  level 
and  not  at  the  ground,  indicates  that  it  is  the  cloud  temper- 
atures which  must  be  studied  for  synchronism  rather  than  those 
of  the  free  air  near  the  surface  of  the  earth.  It  is  evident  that 
a  large  task  in  observations  must  be  executed  by  meteorolo- 
gists before  the  details  of  these  processes  can  be  satisfactorily 
worked  out. 

From  what  was  written  in  my  report  on  Eclipse  Meteorology 
and  Allied  Problems  regarding  the  iouizationof  the  atmosphere 
and  the  formation  of  electric  potential,  it  becomes  evident  that 
temperature  changes  occur  when  the  molecular  structure  of 
the  aqueous  vapor  of  the  atmosphere  undergoes  modification 
by  breaking  up,  at  least  temporarily,  into  atoms  and  ions. 
Since  the  transition  from  water  vapor  to  liquid,  in  cloudy  con- 
densation, marks  a  sensitive  condition,  and  since  it  is  just  at 
this  instant  that  the  terrestrial  (not  solar)  radiation  is  most 
absorbed,  therefore  all  the  conditions  favor  an  excessive 
generation  of  ions  and  a  change  in  the  electric  potential 
gradient.  The  fact  that  this  element  follows  strictly  the 
two  type  periods  seen  in  the  humidity  and  the  barometric 
pressure  makes  it  necessary  that  the  absorption  of  energy  and 
the  ionizatiou  should  be  resultant  functions  occurring  together 
in  one  general  process.  I  believe  that  all  the  complex  details 
observed  regarding  atmospheric  electricity  will  be  explained 
along  these  lines.  Finally,  in  fig.  2,  it  is  indicated  that  the 
diurnal  deflecting  wind  components  and  the  magnetic  deflecting 
vectors  of  the  earth's  field  are  in  close  synchronism  through- 
out the  twenty-four  hours,  but  by  comparing  them  with  the 
diurnal  radiation  of  the  sun  and  the  temperature  it  is  seen  that 
they  are  simply  parts  of  the  single  period  system  which  is 
common  to  all  strata  of  the  atmosphere,  except  the  lowest,  in 
the  three  elements  described,  namely,  the  barometric  pressure, 
vapor  tension,  and  electric  potential  gradients.  We  infer, 
then,  that  since  the  double  period  depends  strictly  on  the  con- 
vectional  rise  and  fall  of  the  vapor  sheet,  the  magnetic  field  is 
primarily  more  closely  connected  with  the  effects  of  the  solar  di- 
rect radiation  throughout  the  atmosphere.  What  we  lack  in  this 
connection  is  a  series  of  observations  to  determine  the  varia- 
tion of  the  magnetic  components  in  the  higher  strata,  which  I 
doubt  not  will  be  found  to  be  similar  to  those  at  the  surface. 
In  all  respects  it  is  evident  that  observation  in  the  lower  cloud 
region  is  as  much  demanded  by  the  maguetician  as  by  the  me- 
teorologist, to  determine  the  subtle  cross  connections  between 
the  gaseous  contents  of  the  atmosphere  and  the  electrical  and 
the  rnagnetical  variations.  But  it  seems  to  me  very  probable 
that  the  magnetic  diurnal  variations  are  due  to  a  set  of  phys- 
ical processes  induced  by  the  terrestrial  radiation  in  the  lower 
atmosphere.  This  may  explain  the  fact  that  the  incoming  solar 
radiation  does  not  seem  to  be  the  cause  of  the  ionizatiou  which 
apparently  precedes  the  generation  of  the  electric  and  the 
magnetic  disturbing  forces.  If  this  problem  can  be  solved  in 
the  free  air,  it  will  probably  also  contribute  important  facts 
regarding  our  general  knowledge  of  the  relations  between 
matter  and  ether.  It  is  especially  desirable  to  note  that  the 
facts  which  are  now  known  indicate  that  the  diurnal  variation  of 
the  magnetic  field  of  the  earth  is  strictly  a  meteorological  effect 
in  the  atmosphere,  caused  by  the  solar-terrestrial  radiation,  and 
that  the  orcler  of  production  is  (1)  temperature,  (2)  electric 
potential,  (3)  magnetic  deflection,  somewhat  as  explained  in 
Bulletin  I,  Eclipse  Meteorology  and  Allied  Problems. 


II.— SYNCHRONOUS  CHANGES  IN  THE  SOLAR  AND  TERRESTRIAL  ATMOSPHERES. 


Read  before  Section  A,  Astronomy  and  Astrophysics,  American  Association  for  the  Advancement  of  Science.    Washington,  D.  C.,  December  28, 1902. 


GENERAL    REMARKS. 

Iii  my  paper,  "A  contribution  to  cosmical  meteorology," 
published  in  the  MONTHLY  WEATHER  REVIEW  for  July,  1902, 
evidence  was  given  of  the  fact  that  the  variation  in  the  solar 
output,  as  registered  in  the  relative  frequency  of  the  sun  spots, 
has  a  marked  synchronism  with  the  variation  of  the  areas  in- 
closed by  the  curves  representing  the  horizontal  magnetic 
force  of  the  terrestrial  field.  This  is  of  course  well  known 
from  many  investigations,  but  the  special  features  of  the 
paper  showed  that  the  sun  spots  constitute  only  a  sluggish 
register  of  the  solar  activity,  and  that  the  terrestrial  magnetic 
force  exhibits  a  set  of  characteristic  minor  fluctuations  super- 
posed upon  the  general  11-year  curve.  These  special  varia- 
tions reappear  with  marked  distinctness  in  the  solar  promi- 
nences as  measured  by  their  observed  frequency,  and  also  in 
the  variations  of  the  mean  annual  barometric  pressures  in  all 
portions  of  the  earth.  The  significance  of  this  exhibit  is  its 
indication  that  the  pressures  in  the  earth's  atmosphere  are 
undergoing  changes  in  short  cycles  of  about  three  years 
average  duration,  which  correspond  with  the  changes  iii  the 
external  work  of  the  sun.  A  further  study  of  our  meteorological 
records  during  the  past  few  month  convinces  me  that  these 
short  cycles  are  produced  by  modifications  in  the  general 
circulation  of  the  earth's  atmosphere,  which  produce  alternate 
accelerations  or  retardations  of  general  movements,  and  that 
these  raise  or  lower  the  average  annual  barometric  pressure 
over  large  districts  of  the  earth's  surface.  There  is  also  a 
sort  of  surging  of  the  atmosphere  with  more  or  less  stationary 
configurations  or  structures,  and  these  involve  the  so-called 
seasonal  climatic  changes  of  weather  by  which  one  year  dif- 
fers from  another.  Thus,  the  regions  about  the  Indian  Ocean 
and  South  America  vary  synchronously  but  inversely;  the 
continental  and  the  ocean  areas  appear  to  change  in  an  inverse 
manner;  there  seems  to  be  a  tendency  to  generate  a  great  cyclic 
change  having  a  period  of  about  eight  years  within  which 
the  pressure  excesses  begin,  for  example  in  India,  pass  through 
Asia,  Europe,  North  America,  and  South  America  back  to 
India.  This  synchronism  between  the  solar  and  terrestrial 
variations  is  found  in  the  United  States  to  hold  for  the  pres- 
sures, temperatures,  the  storm-track  movements  in  latitude 
and  longitude,  the  cold-wave  tracks,  and  generally  for  all 
the  elements  of  the  atmosphere.  I  have  elsewhere  sufficiently 
described  my  views  regarding  the  causes  of  this  synchronism, 
and  it  must  be  evident  to  all  that  meteorology  has  a  great  in- 
terest in  elucidating  these  fundamental  problems  of  solar 
physics,  since  our  hope  of  making  seasonal  forecasts  of  the 
weather  will  be  fulfilled  only  by  reducing  our  knowledge  of 
the  complex  connections  between  the  sun  and  the  earth  to  a 
scientific  basis.  I  can  at  this  time  present  the  result  of  only 
one  portion  of  my  work  in  this  direction,  with  an  indication 
of  the  nature  of  the  problems  that  must  be  solved  by  astro- 
physicists in  order  to  perfect  our  knowledge  of  terrestrial 
meteorology. 

DISTRIBUTION    IN    LONGITUDE. 

It  is  desirable  to  study  the  distribution  of  the  effects  of  the 
solar  activity  at  the  surface  of  the  sun  in  both  longitude  and 
latitude,  and  their  variations  in  the  11-year  period.     Passing 
BIG 2 


over  the  subject  of  the  true  period  of  the  sun's  rotation,  which 
is  now  being  discussed  by  scientists,  and  which  would  require 
a  longer  statement  than  is  here  possible,  it  may  be  noted  that 
whatever  period  is  adopted  for  an  ephenieris,  the  frequency 
numbers  for  spots,  faculse,  and  prominences  collected  in  tables 
will  show  a  drift  to  the  right  or  left  according  as  the  period 
is  too  short  or  too  long.  For  example,  if  in  constructing  an 
ephemeris  one  adopts  as  the  mean  period  of  rotation  that 
which  is  proper  to  the  sun  spots  at  latitude  <p  =  12°,  which  is 
25.23  (siderial)  days  with  the  diurnal  angle  14.27°,  as  Sporer 
and  Wolfer  have  done,  and  collects  together  the  faculae  in 
longitude,  it  is  found  that  charts  of  successive  rotations  of 
the  sun  on  this  ephemeris  show  a  trend  to  the  right  for  the 
years  1887-1889,  but  a  trend  to  the  left  in  the  years  1890-1892. 
This  is  due  to  the  fact  that  just  preceding  the  minimum  of 
the  solar-spot  and  faculse  period,  these  formations  occur  chiefly 
in  low  latitudes,  within  5°  to  10°  of  the  solar  equator,  but 
after  the  minimum  in  latitudes  20°  to  25°.  In  the  former  set 
the  rotational  period  is  much  shorter  than  in  the  latter,  that 
preceding  minimum  being  shorter,  and  that  following  mini- 
mum being  longer,  than  the  period  at  12°  latitude.  Thus 
Wolfer  finds  the  diurnal  angle  of  rotation  14.41°  (or  rotational 
period  24.98  days)  in  latitude  5°,  but  13.92°  (with  period  25.8(5 
days)  in  latitude  22°,  as  against  14.27°  (with  period  25.23  days) 
in  latititude  120.1 

Wolfer's  charts  show  a  distinct  trend  to  the  right  for  the 
spots,  faculse,  and  prominences  during  the  years  1887-1889, 
but  to  the  left  for  the  years  1890-1892.  In  the  case  of  the 


DirectType 
Sun  Spots  oft  if&e 


i 


^ 


FIG.  1.— Comparison  of  the  total  sun-spot  areas,  1854-1891,  with  the 
magnetic  curves  in  the  26.68-day  period. 

prominences,  which  occur  in  all  latitudes  of  the  sun,  we  may 
expect  to  have  an  opportunity  to  discuss  the  surface  rotation 
in  higher  latitudes  than  those  of  the  spots  and  faculse,  since 
these  are  confined  to  the  zones  ±  30°.  I  am  engaged  in  such 
compilation  of  the  data  of  the  prominences  observed  in  Italy 
from  1871  to  1900,  but  am  not  able  to  make  any  further  state- 
ment at  present.  It  is  evident  that  whatever  fundamental 
rotation  period  may  be  selected  it  can  be  corrected  by  the 
tabular  drift  as  just  indicated.  There  is  to  be  noted,  how- 

1  Publikationeii  der  Steniwarte  des  Eidg.  Polytechiiikums  zu  Zurich. 
A.  Wolfer.     Bd.  I,  II,  III.     1897,  1899,  1902.  9 


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ever,  an  important  feature  of  the  distribution  in  longitude  as 
given  on  Wolfer's  charts,  namely,  that  the  recurrence  of  the 
spots  and  faculse  does  not  happen  at  random  in  all  degrees  of 
longitude,  that  is  on  all  solar  meridians,  but  they  are  arranged 
in  two  well  defined  group  systems,  which  repeat  themselves 
during  many  rotations,  and  these  are  located  approximately 
on  the  extremities  of  a  single  diameter,  that  is,  they  occur 
on  meridians  about  180°  apart.  There  seems  to  be  a  solar 
meridian  plane  on  which  the  output  is  constitutionally  more 
vigorous,  or  as  Wolfer  indicates  the  fact,  the  sun  has  centers 
of  activity  on  opposite  sides  of  its  mass.  This  peculiar  distri- 
bution along  the  equatorial  belt  would  seem  to  imply  that 
the  mass  of  the  sun  tends  to  erupt  more  freely  on  opposite 
sides  of  the  center  along  one  of  its  diameters,  and  this  may 
lead  to  some  knowledge  or  inference  as  to  its  physical  interior 
condition.  It  may  be  a  viscous  mass  somewhat  elliptical  in 
shape,  or  at  least  affording  freer  egress  for  the  escaping  pro- 
ducts of  compression  along  one  axis.  This  phenomenon  is 
best  seen  at  times  of  minimum  activity,  because  near  the  maxi- 
mum the  output  so  far  increases  in  vigor  as  to  be  distributed 
more  equally  in  all  longitudes,  and  to  conceal  this  special  ten- 
dency to  concentrate  along  a  given  axis. 

An  entirely  similar  result  was  obtained  in  my  discussion  of 
the  solar  spots  by  taking  an  ephemeris  based  upon  the  period 
of  the  rotation  at  the  equator,  that  is,  26.68  days  (synodic). 
Compare  Bulletin  No.  21,  Solar  and  Terrestrial  Magnetism, 
Weather  Bureau,  1898,  page  141,  or  Bulletin  I,  Eclipse  Me- 
teorology, page,  91.  The  compilation  of  the  deflecting  vec- 
tors of  the  terrestrial  magnetic  force  gives  a  curve  of  the  same 
type  as  do  the  primary  and  secondary  variations. 

An  inspection  of  the  groups  of  spot  numbers  in  the  tables 
in  which  the  data  were  collected  does  not  indicate  any 
tendency  to  drift  to  the  right  or  left  as  one  passes  through 
the  great  11-year  cycles,  and  this  shows  that  the  spots  have 
sufficiently  short  lives  relatively  to  this  period  to  be  subordi- 
nate to  the  primary  source  of  the  output  from  the  solar  nucleus, 
which  latter  must  have  some  properties  independent  of  the 
observed  surface  phenomena  themselves.  The  angular  velocity 
of  surface  drift  varies  in  latitude,  but  the  internal  action  that 
produces  spots  appears  to  be  united  closely  with  the  observed 
period  at  the  equator  itself,  and  there  is  also  reason  to  believe 
that  the  period  at  the  equator  is  the  same  as  that  at  the  poles. 
The  equatorial  plane  may  be  assumed  to  rotate  with  the  same 
velocity  as  the  interior  mass  and  to  have  the  true  period  of 
rotation.  The  observations  indicate  that  there  is  a  structure 
which  produces  an  excess  of  output  on  certain  meridians 
about  180°  apart.  This  is  the  result  of  our  discussion  of  the 
distribution  of  the  solar  activity  in  longitude,  and  we  will  now 
proceed  to  consider  the  evidence  that  there  is  a  structui'al 
distribution  of  energy  in  latitude. 

DISTRIBUTION    IN    LATITUDE. 

The  Italian  observations  of  the  solar  prominences  made  by 
Secchi,  Tacchiui,  and  Ricco,  from  the  year  1871  up  to  the  pres- 
ent time,  published  in  the  Memorie  della  Societa  degli  Spet- 
troscopisti  Italiani,  constitute  a  valuable  series  of  data  as 
homogeneous  in  character .  as  it  is  possible  to  produce.  A 
shorter  series  by  Rev.  J.  Fenyi,  S.  J.,  at  the  Haynald  Observa- 
tory, Kalocsa,  has  been  published  for  the  years  1884  to  1890, 
inclusive,  and  additional  volumes  of  this  important  work  are 
in  preparation.  Sir  Norman  Lockyer  has  recently  published 
in  volume  70  of  the  Proceedings  of  the  Royal  Society  some 
conclusions  derived  from  the  Italian  data,  but  I  have  for  myself 
collected  together  the  frequency  numbers  for  the  sake  of 
their  bearing  upon  the  problem  of  the  circulation  of  the  mass 
of  the  sun  which  is  about  to  be  described.  Lockyer's  curve 
and  my  own  agree  in  showing  the  same  variation  of  the  annual 
frequency  numbers  for  the  years  1871  to  1900,  inclusive.  My 
compilation  has  been  extended  to  include  the  solar  spots  and 


faculaj  for  the  interval  1880  to  1900.  For  the  years  1872-1877, 
Secchi  collected  his  data  by  periods  of  solar  rotation,  using 
the  period  27.78  days;  for  the  years  1878-1900  Tacchini  and 
Ricco  have  collected  the  data  by  the  calendar  mouths.  I  have 
reduced  the  Secchi  series  to  the  year  intervals,  in  order  to 
make  the  annual  numbers  homogeneous  with  the  Tacchini 
series.  The  number  of  observations  of  the  prominences,  spots, 
and  faculse  has  been  distributed  into  10-degree  zones  in  latitude 
from  the  north  pole  to  the  south  pole  of  the  sun  for  each  rota- 
tion and  month,  respectively,  of  the  two  series,  that  is,  90°  to 

80°,  80°  to  70°, —70°  to  —80°,  —80°  to  —90°.     The  sums 

are  taken  by  zones,  and  also  by  rotations  or  months,  and  are 
checked  by  producing  the  same  annual  sum.  The  annual 
numbers  of  prominences,  spots,  and  faculse,  respectively,  were 
plotted  on  diagrams  in  order  to  exhibit  the  changes  going  on 
in  the  sun  during  the  three  past  11-year  cycles,  but  these 
charts  and  the  expanded  tables  are  not  reproduced  in  this 
present  paper. 

It  was  concluded,  as  the  result  of  a  careful  examination  of 
the  charts,  that  the  average  variation  of  the  output  could  be 
most  satisfactorily  reduced  to  a  law  by  combining  these  three 
cycles  together,  and  thus  eliminating  to  some  extent  two 
sources  of  irregularity,  (1)  that  due  to  the  spasmodic  action 
of  the  sun,  and  (2)  that  caused  by  the  difference  of  cloudi- 
ness from  season  to  season  in  Italy,  which  modified  the  num- 
ber of  days  available  for  the  observations.  The  numbers  are 
collected  in  groups  of  three  years  each,  beginning  1872, 1883, 
1894,  as  shown  in  Tables  1  and  2.  The  years  which  correspond 
with  each  other  in  the  11-year  cycle  are  placed  together,  and  it 
makes  no  difference  where  the  mean  cycle  begins  to  be  num- 
bered. By  passing  down  the  table  from  1872,  three  times  in 
succession,  the  annual  numbers  are  found,  and  can  be  used  in 
other  discussions.  The  data  are  now  exhibited  in  several  ways. 
On  fig.  2  is  given  the  variations  found  by  plotting  the  annual 
numbers  in  each  10-degree  zone  in  succession  for  the  years 
1872-1901.  Thus,  in  the  90°  to  80°  zone  of  the  northern  hemi- 
sphere we  have  from  Table  1  the  numbers  35,  3,  9,  10, 

which  give  the  first  broken  line  of  the  chart.  Viewing  this 
chart  as  a  whole  we  make  the  following  notes:  (1)  The  11-year 
cycle  variation  is  strongly  developed  in  the  equatorial  zones 
and  diminishes  in  intensity  toward  the  polar  zones,  where  it 
has  nearly  disappeared.  (2)  By  plotting  the  mean  annual 
numbers  only  the  prominence  variation  line  is  produced;  see 
the  first  curve  of  fig.  28,  in  my  article  No.  VII,  "A  contribution 
tocosmical  meteorology,"  published  in  the  MONTHLY  WEATHER 
REVIEW  for  July,  1902.  (3)  Although  there  is  considerable  varia- 
tion in  the  amplitude  of  the  same  annual  frequency  number,  that 
is,  in  the  series  of  crests  formed  during  the  same  year  in  differ- 
ent zones,  it  is  evident  that  the  sun  is  affected  throughout  its 
photosphere  by  the  increase  and  decrease  of  the  output  of 
energy  as  registered  in  the  prominence  numbers.  (4)  The  ir- 
regularity, however,  is  so  large  as  to  show  that  the  sun  acts 
like  a  congested  and  discharging  viscous  mass,  through  a 
series  of  distortions,  accelerations,  and  retardations,  in  different 
parts  of  its  mass,  and  that  it  does  not  transfer  its  internal 
energy  into  outside  work  uniformly  and  symmetrically.  It  is 
extremely  important  to  remember  this  because  in  discussing  the 
data  for  the  period  of  the  solar  rotation,  we  do  not  have  a  series 
of  independent  events  to  combine,  as  the  theory  of  least  squares 
or  the  law  of  errors  demands.  It  is  preferable  to  work  out  the 
period  by  methods  more  practical  than  the  application  of  the 
Fourier  series  and  the  Schuster  periodogram,  which  depend 
upon  the  occurrence  of  independent  events,  and  an  expectancy 
based  upon  the  law  of  errors.  The  sun  does  not  exhibit  a 
steady  potential  system  of  either  electric  or  magnetic  forces, 
nor  any  steady  recurrence  of  events  upon  its  surface  which  can 
be  combined  by  rigid  analytic  laws.  This  is  a  natural  conse- 
quence of  the  fact  that  the  mass  of  the  sun  fills  an  immense 
volume  in  space  and  is  experiencing  congestion  and  escape  of 


12 


TABLE  1. — Mean  observed  dixtribution  in  latitude  during  the  11-year  xolar  cyrle.     Solar  prominent-en. 


Years. 

90J 
80 

80° 

70 

70° 
60 

60° 
50 

60° 

40 

40° 
30 

.10° 

•20 

20° 
10 

10° 
0 

0° 
—10 

—10° 

—20 

—20° 
—  SO 

—30° 
-40 

—40° 
—60 

—50° 
—60 

—60° 
—70 

—70° 
—80 

—80° 
—90 

Annual 

Minis. 

(1) 

1872   

35 

39 

47 

106 

164 

218 

229 

225 

207 

216 

246 

270 

234 

184 

120 

33 

34 

38 

2,  645 

1883  

9 

10 

22 

97 

116 

141 

172 

138 

125 

121 

187 

193 

169 

112 

88 

56 

32 

s 

1,  796 

1894       

2 

1 

9 

15 

58 

99 

125 

136 

116 

111 

138 

196 

161 

80 

14 

130 

IIH; 

35 

1  467 

Mean 

15 

17 

26 

73 

113 

153 

175 

166 

149 

149 

185 

220 

188 

Hi'.) 

74 

7.'i 

57 

27 

1  96!l 

(2) 
1873 

3 

10 

38 

107 

107 

181 

206 

165 

175 

201 

235 

182 

188 

106 

92 

40 

7 

10 

2  053 

1884        .   . 

3 

11 

42 

195 

191 

165 

245 

213 

217 

2C,:i 

266 

322 

2<',r> 

164 

ill 

72 

x:i 

4H 

2  sr.i; 

1895  

0 

1 

4 

29 

131 

169 

212 

194 

166 

124 

171 

167 

135 

101 

2(1 

3 

7 

6 

1,640 

Mean   

2 

7 

28 

110 

143 

172 

221 

191 

186 

196 

224 

224 

196 

121 

68 

38 

32 

21 

2  183 

(3) 
1874 

9 

5 

24 

94 

84 

130 

150 

141 

125 

116 

161 

138 

82 

93 

44 

10 

2 

1  415 

1885   

3 

3 

17 

139 

181 

139 

229 

208 

175 

201 

232 

299 

242 

148 

48 

/> 

12 

2 

2,  284 

1896 

6 

3 

4 

37 

93 

141 

131 

100 

53 

89 

147 

151 

117 

92 

28 

9 

7 

3 

1  211 

Mean  

6 

4 

15 

90 

119 

137 

170 

150 

118 

135 

180 

196 

147 

111 

40 

8 

7 

4 

1,637 

(4) 
1875   

10 

13 

15 

87 

60 

46 

78 

81 

55 

26 

61 

52 

44 

61 

137 

19 

5 

6 

856 

1886  

1 

9 

18 

48 

132 

152 

180 

172 

130 

141 

146 

139 

174 

116 

16 

4 

5 

2 

1,585 

1897 

4 

6 

8 

90 

81 

52 

91 

85 

74 

138 

139 

126 

41 

76 

80 

11 

6 

5 

1  113 

Mean  

5 

9 

10 

75 

91 

83 

116 

113 

86 

102 

115 

106 

86 

84 

78 

11 

5 

4 

1,  185 

(5) 
1876  

40 

29 

19 

76 

75 

39 

50 

43 

41 

66 

84 

65 

44 

66 

77 

19 

20 

23 

876 

1887 

12 

15 

15 

99 

162 

161 

178 

136 

96 

134 

140 

192 

156 

287 

70 

9 

12 

3 

1  S77 

1898 

5 

9 

12 

17 

26 

47 

39 

52 

59 

62 

102 

89 

61 

79 

29 

13 

11 

9 

721 

Mean 

19 

18 

15 

64 

88 

82 

89 

77 

65 

87 

109 

115 

87 

144 

59 

14 

14 

12 

1  158 

(6) 

1877 

25 

18 

17 

33 

78 

53 

62 

57 

39 

43 

52 

60 

54 

64 

50 

13 

13 

11 

742 

1888 

8 

16 

25 

49 

117 

152 

99 

116 

75 

110 

155 

216 

220 

317 

176 

16 

15 

5 

1  887 

1899  

5 

10 

11 

16 

23 

13 

17 

24 

24 

31 

56 

57 

54 

82 

31 

17 

21 

6 

498 

Moan 

13 

15 

18 

33 

73 

73 

59 

66 

46 

61 

88 

111 

109 

154 

86 

15 

16 

7 

1  042 

(7) 
1878 

1 

7 

3 

19 

34 

34 

13 

16 

17 

12 

9 

8 

35 

31 

8 

1 

3 

1 

252 

1889  

2 

2 

6 

21 

62 

51 

36 

32 

30 

38 

52 

65 

104 

174 

39 

6 

4 

0 

724 

1900  

5 

9 

16 

36 

30 

18 

19 

25 

27 

35 

31 

32 

31 

96 

CM 

31 

24 

10 

543 

Mean  .  ... 

3 

6 

8 

25 

42 

34 

23 

24 

25 

28 

31 

35 

57 

100 

38 

13 

10 

4 

601 

(8) 
1879 

1 

5 

13 

46 

85 

49 

33 

29 

10 

9 

4 

24 

45 

101 

27 

5 

3 

1 

490 

1890  

3 

1 

0 

19 

75 

66 

29 

22 

11 

15 

30 

69 

96 

185 

61 

1 

0 

2 

685 

Mean  .  .  . 

2 

3 

7 

33 

80 

58 

31 

26 

11 

12 

17 

47 

71 

143 

44 

3 

2 

2 

588 

(9) 
1880 

0 

4 

21 

187 

128 

110 

121 

63 

26 

37 

70 

no 

119 

148 

177 

14 

2 

1 

1  338 

1891  

3 

5 

16 

199 

215 

146 

182 

107 

69 

34 

91 

160 

183 

220 

178 

17 

7 

4 

1  836 

Mean  . 

2 

5 

19 

193 

172 

128 

152 

85 

48 

36 

81 

135 

151 

184 

178 

10 

5 

3 

1  5S7 

(10) 
1881 

5 

13 

143 

169 

107 

132 

175 

153 

93 

76 

126 

197 

191 

116 

170 

115 

15 

2 

1  998 

1892  

0 

23 

247 

137 

119 

172 

207 

136 

98 

124 

154 

252 

272 

183 

283 

62 

2 

1 

2  472 

Mean 

3 

18 

195 

153 

113 

152 

191 

145 

96 

100 

140 

225 

232 

150 

227 

89 

9 

2 

2  235 

(11) 
1882 

21 

146 

177 

56 

108 

160 

196 

193 

133 

114 

168 

198 

157 

172 

118 

141 

63 

g 

2  327 

1893  

0 

10 

25 

29 

93 

187 

206 

158 

132 

149 

195 

229 

226 

138 

208 

242 

13 

1 

2  241 

Mean 

11 

128 

101 

43 

101 

174 

201 

176 

133 

132 

182 

214 

192 

155 

163 

192 

38 

4 

2  284 

heat  energy  generated  by  gravitational  compression.  It  is, 
furthermore,  necessary  to  free  the  solar  data  from  terrestrial 
meteorological  effects  before  any  type  of  least  square  analysis 
can  be  properly  applied.  To  emphasize  this  point  more  fully, 
Tables  3,  4,  and  5,  derived  from  the  original  tabulation,  give 
the  sums  for  each  rotation  or  month,  respectively,  for  the  entire 
solar  surface,  by  summing  up  the  numbers  found  in  the  several 
zones.  It  is  seen  that  in  the  monthly  means  of  the  prominences 
there  is  a  very  distinct  annual  variation  in  the  number  of 
prominences  observed.  This  can  be  due  only  to  the  annual 
change  in  the  Italian  climatic  conditions  which  affected  the 
making  of  the  observations,  and  it  shows  that  the  recorded 
frequency  numbers  are  not  free  from  a  strong  terrestrial  term 
which  must  modify  all  discussions  in  solar  physics,  unless 


satisfactorily  eliminated.  The  tables  for  the  solar  faculse  show 
the  same  seasonal  variation  as  the  prominences,  but  less  con- 
spicuously developed,  while  the  sun-spot  means  are  practically 
unaffected  by  the  climatic  changes.  This  difference  must  be 
attributed  to  the  relative  length  or  duration  of  the  three  phe- 
nomena, the  spots  having  a  life  sufficiently  long  to  bridge  over 
the  gaps  covered  by  cloudy  weather  in  Italy,  so  that  the  true 
number  of  spots  which  occur  on  the  sun  is  really  counted.  This 
is  true  of  the  facultc  to  a  lesser  degree  becaiise  their  lives  arc 
shorter  than  the  sun  spots,  and  some  come  and  go  in  the  intervals 
of  stormy  weather  without  being  enumerated  at  all.  The  promi- 
nence numbers  especially  are  subject  to  loss  by  not  being  ob- 
served continuously,  because  their  life  is  usually  very  brief,  so 
that  the  prominences  which  occur  in  successive  meridian  areas 


13 


Fio.  3. — Mean  variation  of  the  distribution  in  latitude  during  the  11-year  periods  of  the  interval  1872-1900. 


and  are  seen  only  on  the  edge  of  the  sun  can  not  be  fully 
counted  under  ordinary  observing  conditions.  The  Kalocsa 
observations  exhibit  similar  disturbances  due  to  the  conditions. 
If  the  observations  of  1884-1890  be  collected  in  a  similar  mari- 
ner to  that  adopted  above,  we  find  that  the  numbers  increase 
decidedly  from  1884,  which  is  a  maximum  year,  to  1890  which  is 
a  minimum  year,  and  this  is  contrary  to  the  probable  course 
of  the  events.  The  Italian  observations  decrease  from  1884  to 
1890,  and  the  two  series  are  opposite  to  each  other  in  this  re- 
spect, though  they  give  similar  zonal  distributions  so  far  as 
the  maxima  are  concerned.  Steadiness  in  observing  and  elimi- 


nation of  cloudy  weather  was  therefore  indispensable  in  order 
to  procure  reliable  data  for  these  discussions  in  solar  physics. 
So  far  from  being  independent  almost  all  solar  data  are  mutu- 
ally dependent  upon  adjacent  events,  and  Professor  Schuster's 
method  of  the  periodogram  is  subject  to  this  sort  of  limita- 
tion. The  same  is  true  of  almost  all  the  terrestrial  meteoro- 
logical elements,  and  generally  a  negative  result  which  is  de- 
rived from  the  discussion  of  a  periodic  or  cyclic  curve  is  valu- 
able, only  when  it  is  certain  that  the  data  conform  to  the 
analytic  presuppositions,  such  as  are  laid  down  in  the  theory 
of  the  energy  curve.  Schuster  applied  his  theory  to  the  Green- 


14 


TABLE  2. — Mean  observed  dixtribulion  in  latitude  during  the  11-year  aolar  cycle.     Solar  spo<«  and  faculce. 


Yi'lll'v 

.SO  LA  IS  SPOTS. 

SOLAK  KAfl'L^!. 

40° 
30 

30" 
•Ml 

•20° 
10 

10° 
0 

0° 
—10 

—10° 

—  « 

—20° 
—30 

—30° 
—10 

Aunual 
sums. 

Above 
40° 

40° 
30 

30° 

m 

20° 
10 

10° 
0 

0° 
10 

—10° 
-20 

—20° 
—30 

—30° 
-40 

Below 

—  J0° 

Annual 

MIIIIS. 

(l) 

1883  .... 
1894  .... 

Mean  . 

(2) 
1884  

1 
1 

1 

1 

21 
14 

11 
19 

15 

3 

2 

3 

1 

57 
71 

64 

92 

85 

89 

32 
41 

37 

21 
17 

19 

10 
23 

17 

3 
ff 

5 

0 
4 

2 
13 

45 
85 

65 

93 
93 

93 

80 
115 

98 

63 
73 

68 

85 
61 

73 

38 
28 

33 

17 

52 

35 

10 
45 

28 

14 
15 

15 

5 
21 

13 
1 

8 
6 

7 

22 
44 

33 

38 
55 

47 

58 
56 

57 

109 
44 

77 

75 
29 

52 

32 

58 

45 

30 
38 

34 

35 
25 

30 

15 
18 

17 
3 

7 
1 

4 

12 
16 

14 

37 
67 

52 

107 
129 

118 

113 

82 

98 

80 
89 

85 

25 
42 

34 

20 

74 

47 

10 
40 

25 

3 
14 

9 
3 

33 

27 

30 

79 
89 

84 

68 
148 

108 

20 
33 

27 

22 
24 

23 

6 
19 

13 

2 

2 

2 

313 

387 

350 

432 
315 

374 

236 

208 

222 

98 
171 

135 

71 
180 

126 

62 
86 

74 

34 

57 

46 
61 

158 
215 

187 

319 
368 

344 

298 
510 

404 

7 
6 

7 
4 

9 

7 

2 
7 

5 

4 
25 

15 

5 
32 

19 

1 

15 

8 

2 

28 

15 
15 

85 
33 

59 

109 
27 

68 

ISO 

29 

40 

68 
64 

66 

44 

69 

57 

20 
56 

38 

8 
62 

35 

9 

70 

43 

2 
36 

19 

6 
65 

36 
45 

244 
152 

198 

253 
100 

177 

161 
110 

136 

175 
152 

164 

135 
161 

148 

97 
100 

99 

39 
129 

84 

21 
122 

72 

9 

75 

42 

6 
112 

59 
31 

150 
155 

153 

279 
156 

218 

188 
189 

189 

154 
166 

160 

143 
145 

144 

99 
96 

98 

47 
181 

114 

32 
181 

107 

37 
103 

70 

15 
171 

!)3 
6 

45 
37 

41 

121 
112 

117 

107 
148 

128 

117 
154 

136 

174 
121 

148 

164 
129 

147 

70 
207 

139 

53 
226 

140 

71 
130 

101 

30 
211 

121 
11 

21 
12 

17 

58 
61 

60 

85 
154 

120 

159 
199 

179 

168 
167 

168 

169 
209 

189 

63 
197 

130 

39 
200 

120 

38 

118 

78 

19 
168 

N 

16 

124 
71 

98 
196 

169 

174 

163 
238 

201 

89 
139 

114 

69 
104 

87 

40 
156 

98 

23 
96 

60 

7 
133 

70 

2 

62 

32 

12 
90 

51 
44 

146 

83 

115 

187 
167 

177 

120 
173 

147 

24 
53 

39 

11 
14 

13 

2 
45 

24 

3 

27 

15 

1 
53 

27 

793 
941 

867 

748 
791 

77(1 

594 
809 

698 

258 
946 

609 

169 

1,044 

607 

160 
582 

371 

94 
937 

516 
183 

908 
554 

731 

1,341 
869 

1,  102 

923 

1,  1(17 

1,015 

3 
2 

1 
1 

7 
4 

1895  .... 

1 
1 

Mean  . 

(3) 
1885  

2 

1 

1896  .... 

5 
3 

1 
19 

10 

1 
15 

8 

Mean  . 

(4) 
1886  

1 

1 

1897  

3 
•2 

1 
6 

4 

Mean  . 

(5) 
1887  .... 

1 
1 

1898  

Mean  . 

(6) 

1888  

1 

1899  

8 
4 

1 
15 

8 

33 

17 

2 
57 

30 
14 

60 
19 

40 

92 

72 

82 

37 

57 

47 

2 
1 

1 

20 

11 
1 

14 
1 

8 

32 
11 

22 

9 
6 

8 

Mean  . 

(7) 
1889  

3 

8 

1900 

Mean  . 

(8) 
1890  .... 

2 

20 

24 
57 

41 

52 
34 

43 

35 
39 

37 

4 
21 

32 
33 

33 

61 

78 

70 

40 

79 

60 

(») 

1880  
1891  

6 

3 
6 

5 

19 
1 

10 

15 
4 

10 

3 
3 

3 

Mean  . 

(10) 
1881  

6 

1892  .... 

Mean  . 

(ID 
1882  

2 

1 

12 
6 

1893  
Mean  . 

1 
1 

6 
3 

wich  magnetic  declinations  taken  from  day  to  day,  where  the 
hourly  variation  is  eliminated.  It  can  be  shown  that  the  de- 
clination is  a  component  which  vanishes  in  theory,  arid  exists 
in  practise  only  as  a  measure  of  the  feeble  variations  of  the 
earth's  field  which  are  distinctly  accidental  and  only  remotely 
connected  with  the  solar  action. 

VARIATIONS    IN    LATITUDE    IN    THE    11-YEAB    CYCLE. 

\Ve  will  now  consider  the  prominences,  spots,  and  faculse  in 
the  11-year  cycle  in  order  to  discover  whether  there  is  some 
evidence  of  a  periodic  variation  in  the  latitude  at  which  the 
output  from  the  interior  of  the  solar  mass  becomes  visible  to 
us.  An  inspection  of  the  details  of  the  three  cycles  contained 
within  the  interval  of  time  1872-1900,  shows  that  there  is  a 
triple  repetition  of  similar  variations  in  these  elements,  and 
suggests  that  the  mean  values  of  the  years  similarly  placed  in 
the  11-year  period  may  be  taken  as  a  close  approach  to  the 
law  underlying  these  cyclical  changes.  The  means  of  Tables 
1  and  2  are  plotted  on  fig.  3.  The  scale  denotes  the  fre- 
quency numbers  as  counted  from  the  Italian  observations, 


and  the  zones  are  indicated  by  the  degrees  at  the  top  of  the 
chart.  Dotted  lines  are  drawn  through  the  systems  of  the 
maximum  numbers  to  mark  the  difference  in  latitude  at  which 
these  develop.  The  prominences  have  two  distinct  maxima, 
generally,  throughout  the  period,  except  that  the  one  in  high 
latitudes,  60°-70°,  nearly  disappears  at  the  time  of  maximum 
spot  frequency  and  the  one  in  low  latitudes,  20°-30°,  practically 
disappears  at  the  time  of  the  minimum  number  of  spots.  After 
the  minimum  which  has  crests  in  high  latitudes  there  is  a 
vigorous  recrudescence  of  the  prominences  in  two  distinct 
belts  of  maxima,  20°-30°  and  40°-5()°,  with  a  tendency  to  di- 
verge toward  lower  and  higher  latitudes;  the  higher  varies 
'25°  in  latitude  and  the  lower  less  than  10°.  This  swing  in 
latitude  of  the  maximum  points  is  accompanied  by  a  decided 
variation  in  the  number  observed,  as  indicated  by  the  change 
in  the  areas  included  between  the  lines  of  prominence  numbers 
and  the  axis  of  abscissas.  The  spots  and  the  facuhu  have  each 
only  one  maximum  in  the  same  hemisphere,  which  gradually  ap- 
proaches the  equator  from  about  latitude  25°  at  the  time  of  re- 
crudescence just  following  the  maximum  number.  The  dying 


15 


TABLE  3. —Italian  observations.     Observed  mean  monthly  distribution  of  the  solar  prominences. 


Rotation. 

1872. 

1873. 

1874. 

1875. 

1876. 

1877. 

Mean. 

1 

202 

150 

91 

37 

13 

40 

89 

2 

229 

200 

135 

69 

51 

75 

127 

3 

214 

130 

140 

60 

51 

59 

109 

4 

157 

188 

98 

55 

26 

37 

93 

5 

219 

180 

97 

65 

51 

55 

111 

6 

229 

139 

107 

45 

42 

95 

110 

7 

281 

215 

96 

48 

47 

54 

124 

8 

315 

229 

105 

124 

107 

115 

166 

9 

287 

105 

111 

131 

114 

82 

138 

10 

143 

190 

163 

51 

105 

42 

116 

11 

129 

89 

75 

71 

83 

31 

80 

12 

130 

98 

115 

46 

88 

54 

89 

13 

110 

140 

35 

54 

59 

3 

67 

14 

52 

39 

Mouth. 

1878. 

1879. 

1880. 

1881. 

1882. 

1883. 

1884. 

1886. 

1886. 

1887. 

1888. 

1889. 

January 

3 

7 

13 

45 

229 

95 

139 

104 

i  in 

lie 

February 

26 

4 

71 

80 

242 

137 

186 

l')7 

98 

1117 

March  

39 

7 

145 

88 

184 

97 

317 

146 

126 

107 

April  

33 

54 

109 

146 

133 

212 

111 

82 

129 

9fifi 

4.Q 

May     

31 

12 

81 

210 

183 

183 

237 

226 

162 

June  

27 

64 

146 

177 

269 

122 

237 

351 

174 

9*V7 

9(1 

July 

59 

57 

260 

299 

288 

219 

364 

328 

233 

9«Q 

1  ^  J. 

August   

22 

61 

137 

284 

249 

167 

399 

221 

162 

231 

999 

(HI 

September 

80 

137 

187 

169 

133 

233 

177 

140 

1R1 

October 

4 

100 

120 

121 

137 

233 

269 

104 

68 

CO 

1  ^K 

November 

8 

58 

77 

258 

139 

135 

152 

126 

138 

141 

70 

4.7 

December  

40 

97 

140 

92 

142 

111 

193 

77 

108 

7U 

94 

Month. 

1890. 

1891. 

1892. 

1898. 

1894. 

1895. 

1896. 

1897. 

1898. 

1899. 

1900. 

Mean. 

January 

25 

60 

83 

145 

87 

28 

134 

60 

53 

AK 

jii 

QO 

February  
March     

27 
29 

170 
110 

95 
122 

214 
272 

141 
159 

69 
127 

155 
71 

69 

109 

42 
31 

38 
40 

13 

9O 

104 

1  1S 

April 

38 

138 

158 

324 

104 

131 

77 

85 

60 

AK 

09 

May  

31 

98 

207 

143 

114 

141 

103 

84 

26 

18 

AQ 

1  IK 

June    

63 

108 

330 

161 

178 

181 

125 

119 

77 

51 

QC 

14.7 

July 

60 

256 

323 

167 

157 

257 

143 

81 

64 

K9 

I',S 

1  UO 

August      

82 

210 

296 

267 

167 

246 

105 

113 

78 

44 

^fi 

September  

68 

220 

305 

185 

116 

178 

106 

143 

121 

76 

96 

149 

October    . 

175 

217 

186 

138 

78 

93 

102 

101 

86 

\f> 

fin 

November    .     ... 

36 

98 

216 

70 

104 

114 

55 

95 

27 

28 

9ft 

December 

51 

151 

151 

155 

62 

75 

35 

54 

^fi 

1<V 

KA 

or; 

TABLE  4. — Observed  mean  monthly  distribution  of  the  solar  spots. 


Month. 

1880. 

1881. 

1882. 

1883. 

1884. 

1885. 

1886. 

1887. 

1888. 

1889. 

1890. 

January  

15 

20 

28 

29 

56 

26 

g 

6 

7 

3 

February 

5 

19 

27 

19 

32 

37 

y 

7 

5 

4 

1 

March  

9 

19 

32 

14 

43 

16 

18 

6 

4 

4 

9 

April 

6 

38 

27 

32 

35 

19 

14 

5 

g 

I 

g 

Mav. 

9 

34 

24 

23 

37 

23 

g 

g 

2 

1 

g 

June  

10 

25 

16 

26 

28 

28 

11 

g 

3 

1 

4 

July  

13 

54 

27 

22 

42 

1H 

9 

11 

5 

7 

* 
4 

August 

18 

14 

17 

29 

44 

20 

5 

3 

10 

4 

g 

September 

24 

22 

22 

22 

37 

13 

g 

6 

10 

2 

13 

October  

24 

25 

30 

35 

32 

15 

2 

4 

1 

3 

g 

November 

14 

26 

28 

28 

23 

14 

1 

2 

4 

3 

December 

11 

23 

20 

34 

23 

7 

0 

5 

3 

7 

5 

16 


TABLE  4. — Observed  mean  monthly  distribution  of  the  aolar  npol» — Continued. 


Month. 

1891. 

1892. 

1893. 

1891. 

1895. 

18%. 

1897. 

UML 

1899. 

1900. 

Means. 

January  

8 

34 

33 

36 

36 

19 

19 

12 

12 

5 

20 

February 

11 

21 

23 

27 

19 

20 

11 

18 

7 

5 

16 

March  

9 

25 

36 

34 

26 

25 

19 

14 

6 

4 

17 

April  

18 

29 

60 

24 

36 

20 

22 

14 

11 

10 

21 

May  

17 

29 

41 

37 

22 

16 

11 

12 

2 

7 

18 

June 

21 

36 

39 

35 

29 

13 

4 

21 

7 

6 

18 

July  

29 

33 

49 

38 

24 

21 

15 

11 

9 

f, 

21 

August 

20 

28 

66 

38 

28 

11 

10 

10 

2 

2 

18 

September  

23 

29 

49 

41 

30 

23 

•2:t 

13 

6 

7 

20 

October 

22 

44 

49 

19 

24 

16 

1'J 

29 

11 

3 

20 

November 

17 

25 

32 

34 

15 

11 

5 

17 

5 

2 

15 

December  

20 

35 

33 

24 

26 

13 

13 

9 

8 

15 

TABLE  5. — Observed  mean  monthly  distribution  of  the  solar  facukE. 


Month. 

1880. 

1881. 

1882. 

1883. 

1884. 

1885. 

1886. 

1887. 

1888. 

1889. 

1890. 

January  

34 

52 

64 

60 

81 

57 

18 

12 

17 

1 

21 

February  

53 

59 

81 

54 

73 

82 

16 

1C 

7 

1 

12 

March  ... 

109 

87 

92 

45 

74 

64 

30 

20 

17 

4 

13 

April  

29 

123 

76 

57 

61 

42 

25 

9 

14 

4 

7 

May 

47 

150 

80 

61 

50 

58 

40 

15 

8 

g 

15 

June    

57 

128 

79 

56 

67 

63 

40 

24 

12 

7 

12 

July                 * 

74 

181 

116 

39 

68 

41 

32 

15 

14 

12 

14 

August  

81 

141 

80 

58 

64 

46 

13 

14 

18 

24 

17 

September 

136 

161 

64 

92 

66 

56 

18 

9 

24 

12 

27 

October  . 

115 

102 

50 

101 

47 

22 

9 

7 

8 

11 

12 

November  ,  .  .  .  . 

86 

85 

62 

86 

50 

31 

5 

12 

9 

2 

16 

December 

87 

72 

79 

84 

47 

32 

12 

16 

12 

10 

17 

Month. 

1891. 

1892. 

1893. 

1894. 

1895. 

1896. 

1897. 

1898. 

1899. 

1900. 

Mean*. 

January 

8 

52 

68 

79 

54 

56 

63 

83 

34 

73 

47 

February  .    ... 

37 

42 

76 

76 

38 

61 

60 

67 

70 

45 

49 

March 

30 

56 

87 

53 

70 

OK 

65 

78 

31 

71 

55 

April 

43 

71 

91 

57 

88 

89 

83 

62 

39 

76 

55 

May  

52 

75 

119 

68 

49 

75 

69 

132 

48 

52 

60 

Juue 

63 

97 

107 

103 

87 

62 

89 

94 

56 

95 

67 

July  

75 

94 

125 

88 

90 

83 

91 

132 

83 

68 

73 

August  

64 

59 

94 

86 

68 

82 

116 

138 

98 

146 

72 

September 

46 

84 

85 

86 

66 

68 

68 

97 

12 

97 

65 

October  

51 

92 

78 

74 

60 

66 

72 

57 

14 

76 

54 

November  

37 

65 

65 

96 

75 

40 

95 

45 

51 

38 

50 

December  . 

48 

75 

112 

75 

46 

52 

75 

59 

46 

100 

55 

spots  of  an  old  cycle  in  low  latitudes  very  near  the  equator 
occur  while  a  new  series  of  spots  is  appearing  in  the  higher 
latitudes.  Fig.  3  tells  its  story  so  clearly  that  it  is  not  neces- 
sary to  describe  it  in  greater  detail. 

We  can  bring  out  its  meaning,  however,  in  connection  with 
the  probable  internal  circulation  from  the  interior  of  the  sun 
more  distinctly  by  constructing  the  movement  of  the  maximum 
point  of  relative  frequency  in  latitude  during  an  11-year 
cycle  of  the  solar  prominences,  spots,  and  faculse,  see  fig.  4. 
The  point  on  fig.  3  where  the  dotted  maximum  line  crosses 
the  line  of  relative  frequency  fixes  the  latitude  of  the  maximum 
number.  Hence,  we  take  for  coordinates  the  number  from 
the  scale  of  ordinates  and  the  latitude  from  the  abscissas 
(N,  <f)  and  transfer  these  coordinates  in  succession  from  year 
to  year  to  fig.  4.  The  first  point  in  the  prominence  curve  in 
the  northern  solar  hemisphere  is  for  the  year  1894  (A7=  64, 
<f  =  57°),  and  this  is  plotted  at  latitude  57°  at  the  same  scale 
distance  from  the  solar  disk,  as  on  fig.  3  from  the  axis  of 
abscissas,  and  marked  94,  meaning  the  year  1894.  The  suc- 
cessive points  mark  the  locus  of  the  movement  of  this  maxi- 
mum in  the  11-year  cycle.  The  same  method  is  applied  to 
the  two  prominence  systems  of  maxima  in  each  hemisphere, 
and  to  the  single  maximum  of  spots  and  facuhe  in  each  hem- 


isphere, respectively,  the  latter  being  plotted  on  the  left-hand 
side  of  fig.  4  in  order  not  to  confuse  the  drawing.  The  dia- 
gram is  to  be  interpreted  as  representing  the  variations  of 
the  maximum  solar  output  in  belts  or  zones  extending  around 
the  entire  photosphere. 

It  is  instructive  to  note  the  regular  course  that  this  varia- 
tion pursues,  and  this  is  of  fundamental  importance  as  indi- 
cating some  characteristic  conditions  of  the  solar  circulation. 
Beginning  with  the  minimum  years  1889  and  1890,  the  polar 
group  of  prominences  rises  rapidly  until  1891,  turns  quickly 
toward  the  pole  until  1893,  then  diminishes  the  number  and 
gradually  completes  the  circuit,  with  slow  decrease  of  latitude, 
to  1899.  The  southern  polar  group  maximum  traces  quite 
the  same  circuit,  which  has  a  considerable  area  and  a  peculiar 
lip  at  the  years  of  minimum  frequency.  The  equatorial  promi- 
nence group  begins  in  latitude  22°,  rises  quickly  to  a  maximum 
height  in  the  same  latitude,  lingers  nearly  in  the  same  position 
for  several  years  (1893-1895),  with  small  decrease  in  latitude, 
and  is  followed  by  a  gradual  return  to  the  beginning  of  the 
circuit.  The  same  remarks  hold  true  for  both  hemispheres. 
The  equatorial  area  is  long  and  narrow  and  the  polar  approxi- 
mately equilateral  in  form,  showing  that  the  former  changes 
less  in  latitude  than  the  latter,  the  height  being  about  the 


17 


Flo.  4. — Movement  of  the  maximum  point  of  relative  frequency  ill  latitude  during  an  11-year  cycle  of  the  solar  prominences,  spots,  and  faculce. 


same  in  each  ease.  I  have  drawn  some  large  arrows  to  show 
that  a  general  movement  outward  is  indicated  for  latitudes  22° 
to  45°  at  the  recrudescence  of  the  prominences,  and  that  there  is 
a  movement  inward  iu  the  equatorial  and  in  the  polar  latitudes. 
A.  similar  construction  for  the  faculac  shows  that  after  the 
minimum  they  also  spring  up  powerfully  to  their  greatest  fre- 
quency in  latitude  25°,  and  that  they  decline  gradually  with 
diminution  of  the  latitude  till  they  reach  a  minimum,  where 
the  characteristic  double-belt  occurrence  takes  effect.  The 
spots  construct  a  triangular  area,  well  within  that  covered  by 
the  faculae,  and  they  increase  more  slowly  and  decline  more 
regularly  than  do  the  faculae,  while  the  latitude  is  diminish- 
ing. The  heavy  arrows  drawn  on  fig.  4  indicate  an  outward 
impulse  in  the  middle  solar  latitudes  and  an  inward  move- 
ment nearer  the  equator.  This  result  is  in  perfect  harmony 
with  that  obtained  for  the  prominences,  and  we  can  not 
avoid  the  conclusion  that  the  sun  in  cooling  emits  energy  and 
discharges  material  more  vigorously  in  the  middle  latitudes 
than  in  the  polar  and  the  equatorial  regions.  This  suggests 
the  primary  conditions  of  the  circulation  which  prevail  for  a 
large  mass  like  the  sun  cooling  by  discharge  of  matter  and 
by  radiation. 


Care  should  be  taken  not  to  misinterpret  the  long  arrows 
which  have  been  placed  upon  fig.  4.  These  represent  the  di- 
rection of  the  rising  of  the  maximum  points  to  their  highest 
positions  and  then  the  sinking  back  toward  the  surface.  As 
shown  by  fig.  3  the  entire  solar  surface  is  emitting  outward, 
even  when  the  arrow  is  pointing  inward.  Nevertheless,  the 
movements  of  the  maximum  points  in  latitude  and  altitude 
must  be  attributed  to  an  excessive  output  of  energy,  and  this 
points  to  a  fundamental  circulation  of  the  heat  energy  and  of 
the  material  substances  in  the  sun.  The  next  problem  in  solar 
physics  is  to  discover  the  laws  that  control  this  special  varia- 
tion of  the  distribution  of  energy. 

It  is  proper  in  this  connection  to  reproduce  the  lines  of  the 
Helmholtz-Emden  thermal  structure,  already  noted  in  Bulletin 
I,  Eclipse  Meteorology  and  Allied  Problems,  p.  71.  The  in- 
terior curves  computed  from  Helmholtz's  equations  harmonize 
so  happily  with  the  exterior  lines  derived  from  this  discussion 
on  the  output  of  the  sun,  that  the  probability  is  strengthened 
that  this  scheme  is  the  proper  one  with  which  to  enter  upon 
the  analysis  of  the  internal  circulation  of  the  sun.  As 
already  noted  in  that  bulletin,  if  the  vortex  law  (u>m'  =  constant, 
where  or  =  the  radius  and  u>  =  the  angular  velocity)  holds 


BIG- 


-3 


18 


good  in  this  case,  then  we  have  an  explanation  of  the  cause  of 
retardation  of  the  diurnal  angular  velocity  of  the  motions  of 
the  photosphere  in  middle  latitudes  as  referred  to  the  equato- 
rial or  polar  belts.  For  if  «,>  &l  then  «>,<<«,,  and  since  w, 
is  the  initial  rotational  velocity  at  the  equator,  the  angular  ve- 
locity in  middle  latitudes  must  be  less  than  at  the  equator  or 
at  the  poles.  This  agrees  with  the  result  of  the  surface  ob- 
servations. Furthermore,  the  equatorial  angular  velocity  is 
probably  that  of  the  interior  mass,  or  micleus  of  the  sun,  and 
the  poles  should  have  the  same  velocity,  a  result  in  harmony 
with  that  deduced  from  my  discussion  of  the  terrestrial  mag- 
netic field.  This  equatorial  and  polar  angular  velocity  gives 
a  26.68-day  synodic  period  for  the  rotation  of  the  sun.  Finally, 
the  middle  latitudes  must  give  a  slower  angular  velocity  and 
a  greater  period,  such  as  27.30  days  in  the  belts  12°  to  15°. 


Since  the  mass  of  the  sun  ought  not  by  this  theorem  to  have 
in  any  portion  of  it  an  angular  velocity  less  than  that  of  the 
equatorial  plane,  it  does  not  appear  to  be  reasonable  that  the 
short  periods  of  about  25.80  to  26.00  days,  which  several  inves- 
tigators have  announced  as  that  of  the  sun's  rotation  derived 
from  a  discussion  of  several  different  terrestrial  phenomena, 
can  be  correct.  It  is  very  difficult  to  perceive  how  there  can  be 
any  basis  for  a  period  shorter  than  26.G8  days;  on  the  contrary 
these  authors  seem  to  find  a  period  at  least  one  day  shorter 
than  the  quickest  period  that  can  be  derived  from  the  obser- 
vations and  discussions  of  surface  solar  phenomena.  It  is  very 
probable  that  the  problem  of  the  circulation  within  the  sun 
must  be  worked  out  before  we  can  hope  to  bring  that  of  the 
rotation  of  the  solar  mass  to  a  satisfactory  understanding. 


III.— THE  STRUCTURE  OF  CYCLONES  AND  ANTICYCLONES  ON   THE 

STATES. 


3500-FOOT   AND   10,000-FOOT  PLANES  FOR  THE  UNITED 


The  reconstruction  of  tlie  theory  of  cyclones  and 
anticyclones  depends  upon  the  determination  of  the 
velocities  and  directions  of  the  air  movements,  the 
form  of  the  isobars,  and  the  distribution  of  the  iso- 
therms at  several  planes  above  the  sea  level.  My  re- 
port on  the  International  Cloud  Observations  of 
1898-99  gives  the  result  of  the  survey  of  the  upper  air 
for  the  vectors  of  motion ;  this  was  supplemented  by 
a  series  of  papers  in  the  MONTHLY  WEATHEK  REVIEW, 
January  to  July,  1902.  My  report  on  the  Barome- 
try  of  the  United  States,  Canada,  and  the  West 
Indies,  1900-1901,  has  provided  the  necessary  means 
for  reducing  the  observed  station  pressures  to  three 
standard  planes.  The  observational  requirements  of 
the  problem  will  be  completed  by  the  discussion  of 
the  temperatures  and  vapor  tensions,  which  has  been 
already  begun,  though  it  will  take  considerable 
labor  to  finish  the  research.  Meanwhile,  it  is  profit- 
able to  make  use  of  the  material  at  hand  in  a  series 
of  studies  on  the  circulation  of  the  atmosphere  at 
different  levels  up  to  two  or  three  miles  above  the 
sea  level.  Beginning  with  January,  1903,  the  succes- 
sive MONTHLY  WEATHER  REVIEWS  will  contain  charts 
showing  the  mean  monthly  isobars  on  the  sea-level 
plane,  the  3500-foot  plane,  and  the  10,000-foot  plane. 
By  comparing  these  pressures  with  the  series  of 
normal  pressures  given  on  the  charts  of  chapter  7, 
Baroinetry  Report,  we  can  find  the  departures  for 
each  month  on  these  three  planes,  and  a  discussion 
of  such  departures  from  year  to  year,  when  studied 
in  connection  with  other  phenomena,  will  have  an 
important  bearing  upon  the  discovery  of  the  laws 
for  use  in  seasonal  forecasting.  Similarly,  monthly 
temperature  charts  are  given,  and  these  are  con- 
structed by  means  of  the  temperature  gradients 
which  can  be  obtained  from  the  data  in  Table  48, 
of  chapter  8,  of  the  same  report,  by  subtracting  the 
values  of  t  from  t0  (sea  level),  /,  (3500-foot),  tt  (10,000- 
foot)  in  succession.  The  latter  temperatures  were 
found  by  a  process  which  eliminated  the  local  ab- 
normalities contained  in  the  observed  station  tem- 
peratures, and  they  have  permanent  value.  The 
surface  temperatures  of  the  several  stations  need  to 
be  further  revised,  and  so  we  can  claim  at  present 
for  the  temperature  gradients  only  an  approximate 
correctness.  This  imperfection  will  not  greatly  in- 
fluence the  position  of  the  mean  isotherms,  but  the 
reduced  temperatures  of  neighboring  stations  do 
not  appear  on  the  maps  quite  as  harmonious  as  we 
hope  to  make  them  by  means  of  the  revision  just 
mentioned. 


21 


/<*>• JO'- 


7O" 6V 


Of* &)• 


EXAMPLES    OF    SELECTED    CYCLONES. 

The  construction  of  average  vectors  of  motion  and 
of  mean  isotherms  as  contained  in  the  two  reports  on 
Clouds  and  Baronietry  produces  a  composite  or  result- 
ant chart,  and  this  is  of  value  in  discovering  general 
relations  and  laws  of  structure  in  cyclones  and  anti- 
cyclones. It  is,  however,  essential  to  determine  the 
conditions  prevailing  in  individual  cyclones  and  anti- 
cyclones if  we  wish  to  apply  the  theories  of  hydrody- 
namics and  thermodynamics  in  detail,  so  as  to  com- 
pute the  relations  between  the  dynamic  and  thermal 
energies  on  the  one  hand  and  the  resulting  forces 
that  characterize  the  actual  storm.  For  this  pur- 
pose the  station  reduction  tables  of  chapter  9  have 
been  expanded,  and  tables  have  been  furnished  to  the 
several  stations  for  practical  service.  By  means  of 
these  the  observers  at  175  stations  are  enabled  to 
mail  postal  cards  daily  to  Washington  containing 
the  (B,  t,  i')  at  the  station  and  the  reduced  values 
of  the  pressure  for  the  three  planes,  respectively. 
With  this  data,  beginning  December  1,  1902,  we 
have  prepared  daily  charts  of  pressure  for  the 
United  States  and  Canada  on  the  sea  level,  the 
3500-foot  plane,  and  the  10,000-foot  plane,  and  we 
propose  to  discuss  this  material  briefly  in  the 
MONTHLY  WEATHER  REVIEW  preparatory  to  making  a 
suitable  general  report  on  the  entire  subject.  Prof. 
E.  F.  Stupart,  Director  of  the  Canadian  Meteoro- 
logical Office,  is  courteously  cooperating  with  the 
United  States  by  furnishing  the  daily  postal  cards 
for  Canada. 

For  the  month  of  January,  1903,  we  present  two 
cyclones — that  of  January  2,  central  in  the  west 
Gulf  States,  and  that  of  January  7,  central  in  the 
Lake  region — in  order  to  illustrate  typical  configu- 
rations of  the  isobars  on  the  upper  planes.  It  is 
our  intention  to  merely  mention  some  of  the  salient 
features  of  these  charts,  since  an  inspection  of  them 
will  doubtless  suggest  their  true  meaning  to  mete- 
orologists better  than  any  verbal  description.  They 
have  special  scientific  interest  from  the  fact  that  this 
is  the  first  exhibit  of  the  isobaric  systems  in  the 
upper  air  surrounding  individual  cyclonic  and  anti- 
cvclonic  centers. 


22 


January  2, 1903. — Charts  1,  2,  and  3  are  transcripts 
of  the  isobars  as  derived  by  computation  in  accord- 
ance with  the  system  contained  in  the  Barometry 
Report.  We  note  (1)  that  the  closed  isobars  of  the 
cyclone  at  sea  level  tend  to  diminish  in  number  and 
intensity  at  the  upper  levels  and  that  they  finally 
open  out  into  shallow,  inflected  curves  at  the  height 
of  about  two  miles;  (2)  these  curves  in  opening  out 
first  form  cusp-shaped  curves,  joined  together  by  a 
pressure  which  is  higher  than  that  north  or  south 
of  it,  whereby  one  closed  isobar  and  one  long  or 
open  isobar  of  the  same  name  occur  above  and  be- 
low the  line  of  the  cusps;  (3)  the  high  pressures  to 
the  east  and  west  of  the  cyclone  diminish  in  area 
and  soon  fade  away  into  the  long,  looping  isobars 
of  the  upper  strata. 

We  now  find  the  general  normal  and  the  local 
departure  components  of  these  observed  isobars  as 
follows:  (1)  The  normal  isobars  for  the  month  are 
copied  on  tracing  paper  in  black  lines,  being  ex- 
tracted from  the  January  charts  of  chapter  7;  (2) 
these  lines  are  laid  over  the  observed  isobars,  and 
a  new  system  of  lines  is  constructed  by  tracing  the 
diagonals  of  the  quadrilateral  figures  thus  formed, 
and  these  new  lines  are  shown  in  red  lines  on  Charts 
4, 5,  and  6.  These  curves  give  us  in  tenths  of  an  inch 
the  values  of  the  local  pressure  disturbances  which 
deflect  the  normal  isobars,  and  they  therefore  measure 
the  pressure  effect  of  the  local  cyclone  proper.  The 
causes  that  produce  these  local  departures  of  pres- 
sure must  be  the  same  as  those  that  produce  the 
cyclone  itself.  We  may  assume  that  the  upper  vec- 
tors of  motion  are  parallel  to  the  observed  isobars, 
and  we  conclude  that  in  this  particular  storm  a  cur- 
rent of  air  from  the  southeast  is  flowing  upon  the 
United  States ;  that  a  part  of  it  curls  to  the  left  and 
enters  the  vortex  of  the  closed  isobars,  which  gen- 
erates a  vertical  component,  and  that  the  rest  of 
this  stream  flows  away  by  uniting  with  the  normal 
general  circulation.  There  seems  to  be  also  a  minor 
stream  of  air  from  the  northwest,  and  a  portion  of 
this  enters  the  vortex. 


w  AJSt-_j>Jt!__     x-       as- *i_  E <» 


23 


.Iitituari/  7,  1002. — Charts  7,  8,  and  9,  are  trans- 
cripts of  the  reduced  pressures  obtained  in  the  same 
wav;  Charts  10,  11,  and  12  give  the  normal  monthly 
isobars,  and  the  local  isabuormals  of  pressure  of  a 
typical  cyclone  central  in  the  Lake  region.  Here, 
again,  the  central  closed  isobars  open  out  first  into 
cusps  with  a  feeble  high  pressure  bridge,  and  then 
into  loops  which  become  flatter  with  the  height,  and 
finally  disappear  by  merging  in  the  normal  lines. 
It  is  apparent  that  on  the  west  side  of  the  center  a 
strong  current  from  the  north  is  chiefly  concerned 
in  building  this  cyclone,  a  part  of  it  curling  into 
the  central  vortex  which  has  a  vertical  component, 
the  remainder  escaping  eastward  into  the  normal 
circulation.  By  comparing  the  vectors  of  Chart  23, 
International  Cloud  Report  (blue  arrows),  we  see 
that  those  vectors  conform  very  closely  to  these  iso- 
bars, and  that  they  are  generally  parallel  to  each 
other.  The  component  vectors  of  figs.  6  and  7, 
MONTHLY  WEATHER  REVIEW,  March,  1902,  show  that 
the  deflecting  vectors  also  follow  closely  parallel 
with  the  isabuormals  of  pressure.  The  agreement 
of  these  three  independent  researches  assures  us 
that  the  analysis  of  the  structure  presented  in  my 
previous  papers  harmonizes  closely  with  the  observed 
facts.  It  is  evident  that  if  a  series  of  coaxial  circles 
about  the  center  of  the  cyclone  be  superposed  upon 
a  system  of  parallel  lines  representing  the  general 
isobars,  we  should  obtain  resulting  curves  similar  to 
those  that  have  been  produced  by  reduction  of  the 
pressures  from  the  surface  data.  This  involves  an 
equation  of  three  degrees  and  three  characteristic 
areas,  one  central,  one  above  the  cusp  lines,  and  one 
below  them.  (Compare  fig.  11.)  This  analysis  will 
therefore  enable  us  to  pursue  the  mechanics  of  cy- 
clones into  remote  details,  and  so  we  shall  at  length 
be  able  to  compare  theory  and  observation  with  much 
precision.  The  subject  will  be  further  illustrated 
and  discussed  in  later  papers. 


IV.— THE  MECHANISM  OF  COUNTERCURRENTS  OF  DIFFERENT  TEMPERATURES  IN  CYCLONES  AND  ANTICYCLONES. 


THE  WEATHER  BUREAU  CLOUD  OBSERVATIONS. 

The  report  on  the  international  cloud  observations  of  May  1, 
1896,  to  July  1, 1897,  Report  of  the  Chief  of  the  Weather  Bureau, 
1898—99,  Vol.  II,  contained  an  outline  description  of  a  theory 
of  the  structure  of  cyclones  and  anticyclones,  which  was 
thought  to  be  indicated  as  the  probable  interpretation  of  the 
motions  of  the  air  in  cyclones  and  anticyclones.  It  was  evi- 
dent that  a  more  complete  insight  into  the  mechanism  of  this 
type  of  motion  in  a  fluid  under  atmospheric  conditions  would 
be  afforded  by  the  construction  of  systems  of  isobars  on  at 
least  three  planes  having  different  elevations.  For  this  pur- 
pose the  sea  level,  the  3500-foot  level,  and  the  10,000-foot 
level  were  selected,  and  suitable  reduction  tables  have  been 
made  as  described  in  the  report  on  the  barometry  of  the  United 
States,  Canada,  and  the  West  Indies,  Report  of  the  Chief  of 
the  Weather  Bureau,  1900-1901,  Vol.  II.  Since  December  1, 
1902,  we  have  received  daily  reduced  pressures  on  these  planes 
from  the  regular  stations  of  the  United  States  and  Canada, 
and  the  corresponding  charts  have  been  drawn  with  care  by 
Mr.  George  Hunt  of  the  Forecast  Division.  A  definitive  treat- 
ment of  the  problem  evidently  requires  charts  of  the  isotherms 
on  the  same  planes,  but  it  will  not  be  necessary  to  wait  for  the 
completion  of  our  discussion  of  the  temperatures,  because  we 
have  already  obtained  the  approximate  gradients  needed  in  a 
preliminary  study  of  this  question.  It  is  proposed  to  sum- 
marize the  present  status  of  the  research,  previous  to  working 
out  an  analytic  treatment  of  the  mechanism  of  tornadoes,  cy- 
clones, hurricanes,  and  the  general  circulation,  from  the  data 
now  in  possession  of  the  Weather  Bureau. 

THE    GENERAL    CIRCULATION. 

The  circulation  of  the  atmosphere  has  been  analyzed  by 
meteorologists  into  (1)  the  general  cold  center  cyclone,  which 
covers  a  hemisphere  of  the  earth  from  the  pole  to  the  equator, 
and  (2)  the  local  warm  center  cyclones  and  the  anticyclones, 
which  drift  eastward  in  the  temperate  latitudes.  Ferrel 
worked  out  his  well-known  canal  theory  for  the  general 
cyclone,  with  northward  motions  in  the  upper  and  southward 
motions  in  the  lower  strata  of  the  atmosphere.  This  theory 
was  adopted  by  Oberbeck  and  carried  out  with  difference  of 
details,  and  it  has  been  the  prevailing  view  till  the  discussion 
of  the  Weather  Bureau  observations  of  1896-97  in  the  United 
States  proved  that  it  is  incorrect  and  must  be  greatly  modified. 
No  northward  movement  of  importance  exists  in  the  upper 
strata,  and  there  is  no  calm  belt  separating  the  eastward  drift 
from  a  westward  current  in  the  polar  zone.  In  the  Tropics 
the  motions  are  substantially  those  deduced  by  Ferrel,  and 
they  result  naturally  from  the  equations  of  motion  on  a  rota- 
ting earth  heated  in  the  equatorial  belt.  Professor  Hilde- 
brandsson's  report  on  the  International  Cloud  Observations 
confirms  these  facts  for  Europe  and  Asia  generally,  and  there- 
fore we  conclude  that  they  are  fundamental,  and  that  the 
canal  theory  must  be  finally  abandoned.  The  Weather  Bureau 
report  showed  that  the  incoming  solar  radiation  of  short  waves 
heats  the  atmosphere  only  a  little,  but  that  it  does  heat  up  the 
earth's  surface.  This  latter  radiates  much  longer  heat  waves 
at  terrestrial  temperatures,  and  thereby  the  lower  strata  of  the 
atmosphere  are  heated  up  by  convection  currents  to  a  distance 
of  two  or  three  miles.  This  heat  energy  is  very  vigorous  in  the 
BIG 4 


Tropics,  and  produces  currents  of  warm  air  which  leak  outward 
and  flow  toward  the  poles  only  in  the  lower  strata  instead  of  in 
the  high  levels,  determining  by  their  motion  the  local  distribu- 
tions of  pressure  near  the  surface  of  the  earth.  By  an  analo- 
gous process  cold  currents  flow  from  the  higher  latitudes 
toward  the  equator  at  low  or  moderate  elevations.  These 
counter  currents  meet  in  the  middle  latitudes,  as  over  the 
United  States,  and  we  have  now  to  study  the  action  of  the 
resulting  mechanism. 

THE    LOCAL    CIRCULATION    IN    CYCLONES   AND    ANTICYCLONES. 

In  order  to  account  for  the  phenomena  observed  in  cyclones 
and  anticyclones,  there  have  been  two  distinct  lines  of  discus- 
sion, (1)  the  thermodynamic  theory  and  (2)  the  hydrodynamic 
theory.  The  former  required  a  warm  central  current  of  rising 
air  to  form  a  vortex.  The  Espy  hypothesis,  that  the  heat  neces- 
sary to  drive  the  vortex  is  derived  from  the  latent  heat  of  con- 
densation evolved  in  changing  aqueous  vapor  into  water  of  pre- 
cipitation, has  been  strenuously  maintained  by  many  students. 
There  are,  however,  numerous  serious  objections  which  can 
not  be  set  aside,  and  these  have  caused  during  the  past  few 
years  a  general  abandonment  of  the  theory  as  a  true  account 
of  the  primary  cause  of  cyclones.  Ferrel  worked  out  his 
theory  by  means  of  a  special  type  of  vortex  with  closed  boun- 
daries, but  this  does  not,  unfortunately,  in  the  least  satisfy 
the  observations,  and  it  has  been  rejected  as  the  result  of  such 
discrepancy.  The  equations  of  motion  admit  of  solution  by  a 
different  vortex,  which  more  nearly  conforms  to  the  require- 
ments of  the  problem,  but  no  driving  force  sufficient  to  sustain 
a  cyclone  was  discovered  before  the  one  suggested  by  the 
Weather  Bureau  research,  so  that  up  to  recent  times  the 
local  vortices  remained  to  be  fully  accounted  for  on  a  sound 
physical  basis.  The  second  theory  of  the  local  circulation 
considers  it  as  simply  a  question  in  hydrodynamics,  where  the 
local  thermal  force  is  subordinate  to  the  driving  action  of  the 
great  whirl  which  gyrates  about  the  pole  as  a  center.  In  this 
view  the  eastward  drift  simply  curls  up  at  places  and  forms 
eddies  in  the  great  current,  and  they  are  borne  along  by  it. 
This  seems  to  be  the  general  idea  adopted  by  Professor  Hil- 
debrandsson  in  his  recent  report.  There  is  undoubtedly  a 
certain  amount  of  dynamic  action  which  enters  into  the  con- 
struction of  cyclones,  but  there  must  also  be  a  powerful  me- 
chanical force  derived  from  the  effort  to  restore  the  thermal 
equilibrium  between  currents  of  different  temperatures.  We 
shall,  therefore,  endeavor  to  trace  out  these  processes  more 
fully  than  it  was  possible  to  do  a  few  years  ago  and  explain  a 
very  probable  theory  of  the  interaction  of  the  forces  that  gen- 
erate and  sustain  these  local  storms. 

THE    ISOBARS   AND    STREAM    LINES    ON    THE    SEA-LEVEL   PLANE,    THE 
3500-FOOT    PLANE,  AND    THE    10,000-FOOT    PLANE. 

It  is  first  necessary  to  recall  briefly  the  results  derived  by 
the  Weather  Bureau  in  its  research  into  this  problem.  A  con- 
sideration of  the  available  meteorological  observations  above 
the  surface  of  the  ground  convinced  me  that  it  would  be  nec- 
essary to  depend  upon  computations  rather  than  upon  direct 
observations,  in  order  to  obtain  the  daily  synoptic  pressures 
and  temperatures  upon  any  given  reference  plane.  Observa- 
tions by  balloons,  kites,  theodolites,  or  nephoscopes  are  indis- 

25 


26 


27 


/JJ*  12V' 


28 


//a*  /osm  /a?"  AS*  SV'  as 


29 


30 


pensable  in  order  to  secure  the  necessary  data  for  making  the 
reductions  and  for  checking  the  results,  but  it  is  not  possible 
to  make  observations  on  any  elevated  plane  in  sufficient  num- 
bers to  construct  a  daily  map  of  the  weather  conditions  with- 
out adding  many  laborious  corrections.  It  was,  therefore, 
apparent  that  suitable  methods  of  computation  must  be  de- 
vised for  this  special  purpose  in  order  to  reduce  the  problem 
to  practise.  The  Weather  Bureau  now  possesses  complete  ba- 
rometry  tables  for  the  isobars  on  three  planes,  and  is  working 
out  the  data  for  the  corresponding  isotherms.  We  have,  how- 
ever, approximate  temperature  gradients  which  can  be  used 
for  the  present,  in  all  the  preliminary  discussions.  The  ther- 
modynamic  formulse  for  the  a,  /J,  y,  d  stages  have  been  adapted 
to  tables  for  the  computation  of  B,  t,  e  at  different  elevations. 
It  was  indispensable  to  substitute  these  tables  for  the  Hertz 
diagram,  because  that  is  liable  to  an  error  as  large  as  7  milli- 
meters, owing  to  the  neglect  of  the  vapor  tension  in  evaluating 
the  numerical  data.  Since  we  require  vertical  gradients  of 
pressure  to  within  0.01  millimeter,  it  is  practically  impossible  to 
secure  that  degree  of  accuracy  if  the  vapor  tension  is  rejected. 

In  the  MONTHLY  WEATHER  EEVIEW  for  January,  1903,  charts 
of  the  isobars,  figs.  1  to  6  for  January  2,  and  figs.  7  to  12  for 
January  7,  are  given  on  the  three  planes;  the  two  compo- 
nents into  which  they  were  resolved  are  also  charted,  namely, 
the  normal  isobars  for  the  month,  as  given  on  Charts  28,  30, 
and  31  of  the  Barometry  Report,  and  the  local  disturbing  iso- 
bars, which  are  approximately  circular  in  form  at  the  center, 
the  other  lines  having  special  curvatures  which  will  be  ex- 
plained. In  the  present  paper  there  are  similar  charts,  figs.  13  to 
15  for  February  7, 16  to  18  for  February  8,  and  19  to  24  for  Feb- 
ruary 27.  In  order  to  resolve  the  observed  isobars  into  the  com- 
ponents, the  normal  isobars  of  the  month  were  copied  on  trac- 
ing paper;  these  were  superposed  upon  the  computed  isobars 
of  the  given  date,  and  the  diagonals  were  then  drawn  to  form 
the  second  system  of  components.  Attention  should  be  fixed 
upon  one  characteristic  feature  in  these  charts  of  isobars, 
which  is  readily  recognized  on  nearly  every  map.  To  the  north 
or  northeast  of  the  closed  isobars  around  the  low  center,  there 
is  a  cusp-shaped  set  of  isobars  forming  a  saddle  between  two 
isobars  of  the  same  name ;  thus,  on  fig.  19,  the  cusps  30.0  be- 
tween isobars  29.9;  on  fig.  20,  26.4  forms  the  cusps  of  a  sad- 
dle between  26.3;  and  on  fig.  21,  20.2  forms  the  cusps  to  20.1. 

By  referring  to  Maxwell's  Electricity  and  Magnetism,  Volume 
I,  Plate  III,  an  analogue  to  this  typical  construction  in  electro- 
statics is  to  be  found;  his  Plate  I  is  an  analogue  to  a  cyclone 
in  relation  to  the  general  circulation  around  the  pole,  and  Plate 
II  is  an  analogue  to  an  anticyclone.  These  figures  are  con- 
structed by  the  precepts  on  page  169,  so  that  the  resulting 
isobar  is  by  analogy  B=  B^  +  Ev  where  Bt  refers  to  the  gen- 
eral isobars  and  B2  to  the  local  isobars.  In  the  electrostatic 

analogue  the  potential  is  found  by  the  law  V=  —,  where    the 

successive  values  1,  2,  3  are  assigned  to  V,  and  r  is  computed 
from  a  given  value  of  e.  In  the  case  of  the  isobars,  the  dif- 
ferences are  nearly  equal  to  each  other  in  the  general  system, 
and  in  the  local  system  the  gradients  may  be  taken,  for  example, 
about  twice  as  great.  Specifically,  on  the  normal  charts  the 
pressure  difference  is  O  =  0.1  inch  for  about  one  and  three-fifths 
degrees  in  latitude,  or  180,000  meters,  or  112  miles.  A  vigor- 
ous cyclone  is  formed  by  superposing  about  eight  circles,  with 
the  gradient  O  =  0.1  inch  for  four-fifths  of  a  degree,  or  56  miles. 
The  irregularities  arising  from  the  distortion  of  either  typical 
system  give  rise  to  problems  on  the  conditions  of  cyclones  and 
anticyclones  which  are  of  much  interest.  In  the  case  of  elec- 
trostatic force  we  deal  with  potentials  and  lines  of  force;  in 
that  of  pressure  with  stream  lines  and  gradients,  since  in  the 
frictionless  upper  strata  of  the  atmosphere  the  lines  of  motion 
are  parallel  to  the  isobars  unless  under  special  dynamic  con- 
ditions. Now,  on  Charts  36  and  39,  of  the  Cloud  Report,  are 


shown  isobars  after  Teisserenc  de  Bort,  drawn  about  the  pole 
at  the  elevations  1500  and  3000  meters,  respectively.  This  cor- 
responds with  the  system  of  large  circles  in  the  electrostatic 
analogue.  On  Charts  30  and  31,  of  the  Barometry  Report, 
giving  the  normal  pressure  for  the  3500-foot  and  the  10,000- 
foot  planes,  we  have  constructed  the  lines  accurately  for  one 
special  area  in  the  general  system  of  isobars,  namely,  that 
covering  the  United  States,  and  these  are  similar  in  form  .to 
those  from  Teisserenc  de  Bort,  though  numbered  differently  in 
the  inches  on  account  of  changes  in  the  adopted  heights.  They 
are  drawn  as  perfectly  as  possible  and  may  be  trusted  to  rep- 
resent the  result  of  eliminating  the  local  cyclonic  circulations. 
The  maps  of  pressure  and  temperature  given  as  Charts  VIII 
and  IX  of  the  MONTHLY  WEATHER  REVIEWS  for  January  and  Feb- 
ruary, 1903,  agree  closely  together  in  their  curvature  relative 
to  the  pole.  By  comparing  with  these  high  level  isobars  and 
isotherms  the  wind  directions  determined  for  the  upper  cloud 
system,  as  shown  on  Charts  20  to  35  of  the  Cloud  Report,  it  is 
possible  to  infer  that  the  stream  lines  of  the  general  circulation 
are  parallel  to  the  lines  of  equal  pressure  and  temperature  in 
the  higher  strata  of  the  atmosphere.  The  divergences  from 
this  system,  which  occur  at  any  place,  are,  therefore,  not  due 
to  the  action  of  the  forces  of  sliding  friction  such  as  produce 
eddies,  but  to  the  interplay  of  dynamic  forces  of  motion  de- 
rived from  other  sources.  Furthermore,  it  is  simpler  to  de- 
termine the  direction  of  these  common  lines,  the  isobars,  iso- 
therms, and  vectors  of  motion  in  the  upper  atmosphere  by 
computing  the  isobars  and  isotherms  from  the  surface  data 
than  by  the  laborious  compilation  of  wind  directions  and  ve- 
locities by  means  of  cloud  observations,  from  which  the  result- 
ants may  be  deduced.  That  is  to  say,  we  may  have  daily 
stream  lines  on  the  upper  planes  by  computation  from  surface 
data,  which  are  as  reliable  as  those  which  would  be  obtained 
from  a  long  series  of  cloud  observations  reduced  to  annual  or 
monthly  means.  This  is  a  practical  conclusion  of  much  value 
in  meteorology.  The  isobars  on  Charts  37,  38,  39,  40  of  the 
Cloud  Report,  from  the  data  of  Teisserenc  de  Bort,  show  that 
there  is  a  greater  density  of  the  gradient  lines  from  latitudes 
25°  to  60°,  than  nearer  the  equator  or  the  poles.  Therefore 
the  pressure  gradient  is  stronger  over  the  United  States  than  in 
the  tropical  or  in  the  polar  zones.  Such  a  diminution  of  the 
general  gradient  in  lower  latitudes  is  in  accord  with  that  theory 
of  the  general  circulation  which  drives  the  currents  westward 
in  the  lower  strata  of  the  Tropics;  in  the  higher  latitudes  the 
decrease  in  gradient  indicates  a  feeble  tendency  to  form  a  belt 
of  winds  flowing  westward  near  the  pole.  It  is  a  tendency 
only,  because  the  gradient  does  not  reverse  but  continues  to 
diminish  to  the  pole,  and  the  motion  is  everywhere  eastward. 
This  is  another  fact  in  contradiction  to  the  canal  theory,  and 
it  also  implies  that  the  return  circulation  of  cold  air  from  the 
poles  to  the  Tropics  sets  in  near  the  latitudes  of  50°  to  60°  in 
the  descending  anticyclonic  structure,  where  the  cold  streams 
originate  in  connection  with  local  areas  of  high  pressure,  rather 
than  in  the  polar  zone.  The  cyclones  and  anticyclones  in 
middle  latitudes  are  the  natural  products  of  the  thermal  inter- 
change of  heat  between  the  "sources"  which  are  in  the  warm 
currents  and  the  "  sinks  "  which  are  in  the  cold  currents.  This 
is  not  brought  about  through  cooling  a  northward  current  in 
the  highest  strata  of  the  atmosphere  by  its  radiation  of  heat 
into  space,  or  by  vertical  expansion  in  the  Tropics,  as  the  canal 
theory  requires.  The  hot  and  cold  masses  of  air,  so  far  as 
they  are  produced  by  the  differences  of  insolation  in  the 
lower  layers  of  the  atmosphere,  are  brought  together  into 
physical  contact  through  the  low  level  countercurrents,  which 
are  the  winds  from  the  south  and  from  the  north,  respectively. 
These  currents  of  different  temperatures  form  the  natural 
equivalents  to  the  boiler  and  the  condenser  in  a  thermal  en- 
gine, and  the  Carnot  cycle  is  applicable  to  the  analysis  of  the 
cyclic  processes.  The  stream  lines  observed  in  the  motions  of 


31 


FIG.  25. — The  formation  of  local  anticyclones  and  cyclones  in  the  general  circulation  about  the  poles. 


the  atmosphere  as  local  circulations  are  built  up  by  the  struggle 
there  going  on  to  restore  the  thermal  equilibrium  and  uniform 
temperatures.  This  countercurrent  theory  is  an  effective  one, 
in  that  it  brings  the  abnormal  temperatures  of  the  atmosphere 
into  contact  through  the  streams  of  different  temperature,  so 
that  they  can  work  mechanically  upon  one  another.  The 
canal  theory  keeps  the  currents  separated  throughout  the  en- 
tire circuit,  so  that  the  assumed  cooling  and  heating  in  the 
circuit  is  more  like  the  local  heating  of  a  closed  current  at 
one  portion,  while  it  cools  in  traveling  through  the  remainder 
of  its  course.  There  is  little  mechanical  efficiency  in  that  pro- 
cess, and  it  is  not  useful  as  a  meteorological  theory,  nor  in  ac- 
cordance with" the  facts  of  observation. 

A  certain  average  excess  of  heat  in  the  Tropics  is  required 


to  keep  the  general  cyclone  moving  at  its  observed  rate  of 
gyration  in  the  upper  strata.  The  thermal  equator  of  such 
motion  moves  annually  in  latitude  northward  and  southward, 
and  this  carries  with  it  the  entire  thermal  engine  in  its  annu- 
ally changing  configuration.  In  the  northern  winter  the 
thermal  equator  is  far  to  the  south,  the  contrast  between  the 
north  polar  cold  and  the  tropical  heat  is  much  increased,  and 
the  general  cyclone  is  relatively  efficient;  in  the  northern  sum- 
mer the  thermal  equator  is  far  to  the  north,  the  difference  of 
temperature  between  the  boiler  and  the  condenser  of  the 
northern  engine  is  less,  so  that  the  circulation  is  relatively 
feeble.  This  oscillation  of  the  heat  energy  northward  and 
southward,  carrying  with  it  the  thermal  structure  toward  one 
pole  or  the  other,  just  as  the  astronomical  zones  of  day  and 


32 


night  move  up  and  down  the  earth  in  latitude,  is  depicted  in 
the  series  of  diagrams  of  normal  pressure  shown  in  Charts  28 
to  31  of  the  Barometry  Report. 

The  corresponding  variations  of  the  temperatures  are  given 
on  Charts  18,  19,  20,  and  of  the  vapor  tensions  on  Charts  23, 
24,  25  of  the  same  report.  The  functions  of  B,  t,  e,  which  are 
involved  in  these  variations,  constitute  the  basis  for  a  complete 
solution  of  the  forces  that  generate  and  maintain  the  general 
circulation  in  middle  latitudes.  If  we  could  extend  this  sys- 
tem of  pressure  and  temperature  charts  to  the  pole,  and  to 
the  equator  on  the  American  Continent,  and  also  obtain  the 
vectors  of  motion,  it  would  afford  the  required  data  for  the 
discussion  of  the  dynamics  involved  in  the  circulation  of  the 
entire  atmosphere,  and  this  is  the  ultimate  problem  of  our 
meteorology. 

The  variations  of  this  general  circulation  from  season  to 
season  should  be  extended  to  include  its  average  changes  from 
year  to  year,  and  also  the  connection  of  these  with  that  part 
of  the  solar  energy  which  is  expended  as  radiation,  and  is 
variable  in  long  and  short  cycles.  This  will  form  a  science  of 
cosmical  meteorology  upon  which  long  range  forecasting  of 
the  seasons  can  be  based.  Unless  the  subject  proves  to  be  too 
complex  for  human  skill  to  classify,  we  shall  eventually  con- 
struct a  meteorology  rivaling  other  branches  of  astrophysics 
in  interest  and  value  to  mankind. 

THE    MECHANISM    IN    CYCLONES   AND    ANTICYCLONES. 

Turning  now  from  these  considerations  regarding  the  gen- 
eral circulation  to  the  mechanism  of  local  circulations,  we  will 
further  illustrate  the  separation  of  the  local  components  from 
the  general  normal  isobars  by  the  six  diagrams  of  fig.  25,  the 
formation  of  local  anticyclones  and  cyclones  in  the  general  cir- 
culation about  the  pole.  We  draw  18  concentric  circles  about  a 
pole  as  a  center,  where  the  common  difference  is  5  millimeters, 
except  in  the  polar  zone  where  the  difference  is  greater.  The 
outer  circle  extends  to  latitude  23°,  that  is  to  Havana,  so  that 
these  circles  cover  the  latitudes  in  which  the  cyclones  are  pro- 
duced in  northern  latitudes.  Diagrams  1, 2, 3,  show  the  method 
of  constructing  a  low  pressure  area,  and  4,  5,  6,  that  for  a  high 
pressure  area;  diagrams  1  and  4  give  examples  of  the  draw- 
ing of  a  few  individual  resultant  curves;  2  and  5  are  com- 
plete for  isolated  low  and  high  areas;  3  and  6  exhibit  the  con- 
nection between  a  high  and  a  low  area,  and  this  diagram  is  com- 
parable with  the  isobars  found  on  the  charts  of  reduced  pres- 
sures, as  figs.  13,  14,  15,  16,  17,  18,  of  this  paper.  In  making 
these  specimen  diagrams  a  system  of  local  circles  is  superposed 
upon  the  general  circles,  but  the  common  difference  between 
them  is  taken  half  as  much  linearly,  that  is  the  gradient  is  twice 
as  steep.  On  the  general  circles  5  millimeters  is  equivalent  to 
0.10  inch  of  pressure,  on  the  small  circles  2.5  millimeters  is 
equivalent  to  0.10  inch  of  pressure.  These  relative  dimensions 
serve  approximately  to  illustrate  a  strong  winter  cyclone,  but 
they  should  be  modified  according  to  the  observed  conditions 
of  the  individual  cyclone.  When  the  monthly  normal  iso- 
bars are  subtracted  from  the  observed  map  of  a  given  day,  we 
have  at  once  the  small  circular  system,  together  with  its  varia- 
tions from  the  normal  type  according  to  the  prevailing  circum- 
stances. Looking  at  diagram  1,  of  fig.  25,  we  see  that  in 
passing  from  the  pole  outward  each  circle  is  +  0.10,  one-tenth 
inch  higher,  beginning  for  example  with  25.4  and  extending 
to  27.1.  The  small  circles  are  numbered  —  .1,  —  .2,  —  .3,  .... 

for  the  low  area,  and  +  .1,  +  .2,  -f-  .3, for  the  high  area. 

At  the  point  A  we  have  26.1  on  the  large  circle;  on  the  next 
circle  it  becomes,  26.2  —  0.1  =  26.1,  by  uniting  the  two  gra- 
dients; on  the  next  it  is,  26.3  —  0.2  =  26.1.  In  this  way,  draw- 
ing the  diagonal  lines,  we  pass  around  a  U-shaped  curve  hav- 
ing a  certain  concavity.  Other  curves  are  formed  outside  and 
inside  of  it,  a  few  of  the  inner  curves  making  closed  ovals,  ec- 


centric to  the  center.  The  dotted  curve  on  diagram  2 
shows  where  the  cusp-shaped  curves  unite  over  the  saddle  of 
higher  pressure.  The  diagrams  4  and  5  are  drawn  in  a  similar 
way,  by  using  the  plus  system  of  circles.  At  B  we  have 

26.7  +  0.1  =  26.8;    26.6  +  0.2  =  26.8;   26.5  +  0.3  =  26.8 

Similarly  the  other  lines  are  drawn.  Finally,  in  diagrams  3  and 
6  the  two  systems  are  united,  so  that  the  lines  flow  from  one 
to  the  other  continuously.  It  should  be  noted  that  in  fixing 
the  centers  of  the  two  systems  of  component  coaxial  circles, 
that  for  diagram  3  was  placed  on  the  isobar  26.5,  and  that  for 
diagram  6  on  the  isobar  26.4.  That  is  to  say,  the  center  of  the 
anticyclone  must  be  nearer  the  pole  than  that  of  the  cyclone, 
in  order  to  make  the  isobars  continuous,  otherwise  some  of 
the  ends  of  these  systems  of  high  and  low  areas  are  left  un- 
connected and  without  natural  continuity. 

A  comparison  of  these  typical  isobars  with  those  constructed 
from  the  daily  observations,  see  figs.  1  to  24,  proves  conclusively 
that  they  are  substantially  of  the  same  type.  We  find  the 
cusp  formation  on  each  with  the  opening  of  the  U-shaped  figure 
toward  the  pole  in  the  cyclone,  but  toward  the  equator  in  the 
anticyclone.  The  closed  curves  of  the  cyclone  are  more  nearly 
elliptical  than  those  of  the  anticyclone,  as  is  commonly  the 
case  on  the  weather  maps.  The  flow  of  air  from  the  northern 
quadrants  of  the  anticyclone  toward  the  southern  quadrants 
of  the  cyclone  is  necessary  to  the  structure. 

COMPARISON    WITH    OTHER    OBSERVED    CONFIGURATIONS. 

In  order  to  recall  the  results  of  the  research  which  are  in- 
cluded in  the  Cloud  Report,  the  following  drawings  are  intro- 
duced. Fig.  26  shows  the  vectors  of  motion  and  their  com- 
ponents as  observed  in  anticyclones  and  cyclones  at  the  1000 
meter  (3280-foot)  level,  and  the  3000  meter  ( 9843-foot)  level, 
so  that  these  are  comparable  with  the  isobars  computed  on 
the  3500-foot  and  the  10,000-foot  planes.  The  direction  of  the 
original  vectors  is  evidently  parallel  to  the  isobars,  the  long 
vectors  which  indicate  greater  velocity  are  to  the  north  of  the 
anticyclone  where  the  isobars  are  closer,  and  then  to  the  south 
of  the  cyclone  where  the  closeness  of  the  pressure  lines  is  a 
maximum.  Comparing  the  anticyclonic  and  cyclonic  compo- 
nents with  the  resolved  local  isobars  on  the  charts  of  observed 
pressures,  figs.  1  to  24,  the  opening  of  the  stream  lines  marked  .4 
on  the  cyclone  corresponds  with  the  opening  in  the  U-shaped 
clone,  similar  conditions  are  found  to  the  south  of  the  anticy- 
cusps.  Furthermore,  in  fig.  27, 1,  II,  III,  three  charts  are  repro- 
duced from  the  Cloud  Report;  Chart  23,  the  mean  winter  Lake 
region  low;  Chart  29,  the  mean  west  Gulf  low,  each  for  the  lower 
clouds;  and  Chart  35,  the  mean  summer  hurricane  low  for  the 
upper  clouds.  The  stream  lines  flow  uninterruptedly  to  the 
center  on  spiral  or  disturbed  spiral  curves,  one  stream  from  the 
northwest  and  another  from  the  south,  and  to  the  north  of  the 
center  the  same  U-shaped  cusp  formation  is  described  by  the 
vectors  of  motion  as  are  found  on  the  charts  of  isobars.  It  is 
remarkable  that  in  the  case  of  the  hurricane  this  formation  is 
found  in  the  cirrus  levels,  just  such  as  in  ordinary  cyclones 
is  produced  in  the  cumulus  levels,  showing  that  this  funda- 
mental typical  construction  penetrates  to  the  height  of  5  or 
6  miles,  when  the  forces  of  motion  producing  it  are  sufficiently 
intense.  The  relative  penetrating  power  of  the  cyclonic 
action  is  a  very  important  feature,  which  is  brought  out  by 
these  isobars  and  stream  lines  in  the  higher  levels. 

Furthermore,  consider  the  component  local  isobars  in 
dotted  lines  on  figs.  4,  5,  6,  for  January  2;  10,  11,  12,  for 
January  7;  22,  23,  24,  for  February  27.  On  January  2  it 
is  evident  that  the  principal  feeder  is  a  current  of  warm  air 
flowing  over  the  South  Atlantic  States,  which  curls  into  the 
closed  isobars  from  the  northward;  here  the  cusp  formation  is 
somewhat  obscure,  and  this  usually  happens  while  the  center  is 
so  far  to  the  south.  On  January  7  the  main  stream  feeds  into 


33 


the  vortex  from  the  northwest,  and  on  the  western  and  southern 
sides,  where  the  isobars  are  dense,  the  stream  curls  into  the 
center.  On  February  27  there  is  a  strong  stream  from  the 
southeast  and  another  from  the  northwest,  both  of  which  curl 
strongly  into  the  central  vortex. 


Hiffh    urea,   vectors. 


^Anticyclonic  Cbmponents. 


1.86 


O.62 


Jjcnv  area   vectors-. 


Cyclonic  Components. 


miles. 


FIG.  26. — The  vectors  of  motion  and  their  components  in  anticy- 
clones and  cyclones  at  the  1000-mile  and  3000-mile  levels. 

It  should  be  particularly  noted  that  the  stream  curls  into 
the  central  vortex  at  all  levels  from  the  ground  upward,  cross- 
ing the  closed  isobars  at  some  angle,  but  running  parallel  to 
the  open  isobars,  thus  confirming  the  results  of  the  Cloud 
Report. 

It  should  be  observed,  also,  that  the  U-shaped  opening  in 
the  northern  cyclones  is  swung  around  to  the  northeastward, 
thus  distorting  the  lines  from  their  primary  position  of  sym- 
metry, which  is  toward  the  pole.  This  is  due  to  the  fact  that 
the  cyclone  has  vertical  and  gyratory  components  which  pene- 
trate from  lower  to  higher  levels,  and  therefore  into  the 
upper  layers,  drifting  more  rapidly  eastward  than  the  lower, 
BIG 5 


Such  distortion  is  accompanied  by  an  interchange  of  the 
inertia  of  motion,  and  this  is  the  part  of  the  thermal  machine 
of  the  atmospheric  circulation  which  acts  as  a  brake  upon  the 
swiftly  flowing  eastward  drift.  This  is  the  means  by  which 
the  eastward  velocities  are  slowed  down  from  the  excessive 


III. — Summer  hurricane  low.     Chart  35,  International  Cloud  Eeport. 


II.— Winter  west  Gulf  low.     Chart  29,  International  Cloud  Eeport. 


I. — Winter  Lake  region  low.     Chart  23,  International  Cloud  Eeport. 

Fia.  27. — The  stream  lines  at  cumulus  levels  for  cyclones  and  at  cirrus 
levels  for  hurricanes. 

motions  required,  in  the  general  theory  by  the  law  of  the  pre- 
servation of  vortex  areas,  into  the  moderate  motions  actually  ob- 
served. Since  this  penetrating  power  may  extend  to  the  cirrus 
levels,  the  total  energy  of  retardation  is  evidently  very  great, 
and  therefore  this  portio'n  of  the  problem  of  the  general  cir- 
culation should  be  developed  on  the  lines  already  outlined  in 
my  papers,  rather  than  on  those  followed  by  Professor  Ferrel. 
Furthermore,  we  remark  that  my  construction  is  not  in  accord 
with  the  theory  of  the  German  vortex,  as  also  explained  in  that 


report.  This  vortex  requires  a  local  center  of  beat  and  a  vertical 
current,  with  zero  velocity  at  the  center  and  maximum  velocity 
at  a  circle  on  the  edge  of  the  closed  curves,  from  which  locus  it 
gradually  falls  away  to  zero  again  at  a  considerable  distance. 
In  nature  we  have,  on  the  other  hand,  individual  stream  lines 
of  different  temperatures  curling  into  a  common  center,  with 
velocity  increasing  up  to  the  very  center,  as  indicated  on  Chart 
(!9  of  the  Cloud  Report.  The  German  vortex  is  much  nearer 
the  natural  type  than  the  Ferrel  vortex,  but  there  are  features 
in  it  which  are  not  compatible  with  the  observations  them- 
selves. The  disturbance  of  the  eastward  drift  by  the  penetra- 
tion of  a  cyclonic  vortex  into  the  upper  strata  is  further  illus- 
trated by  the  scheme  of  fig.  28,  where  the  successive  levels  are 


Cirrus 


FIG.  28. — Scheme  of  the  disturbance  of  the  eastward  drift  by  the 
penetration  of  a  cyclone  vortex  into  the  upper  strata. 

shown  with  the  isobars  bending  away  from  their  normal  east- 
ward direction,  first  into  U-shaped  curves  about  the  axis,  then 
to  cusps  and  closed  curves,  and  finally  to  simple  closed  curves 
at  the  surface.  These  closed  curves  always  imply  a  vortex 
with  its  vertical  component  governed  by  the  usual  vortex  laws. 
The  boundary  of  the  true  vortex  action  diminishes  in  size,  and 
loses  itself  in  the  upper  strata  as  a  simple  sinuous  deflection. 
The  vortex  throws  up  a  vertical  component  all  over  its  area  in 
proportion  to  the  gyratory  velocity,  and  in  the  center  this 
forms  a  rising  current,  continuous  and  undisturbed,  till  high 
levels  are  attained.  On  the  edges,  however,  the  vertical  com- 
ponent is  stripped  off  by  the  action  of  the  eastward  drift,  which 
also  acts  more  powerfully  in  proportion  to  the  elevation.  This 
depletion  of  the  surface  of  the  vortex  in  proportion  to  the 
height  is  the  mechanical  mode  that  controls  the  escape  of  the 
upward  current,  which  loses  itself  to  the  eastward  by  merging 
in  the  general  circulation,  whence  it  passes  through  other  anti- 
cyclones and  cyclones  in  succession.  The  radial  horizontal 
component  is  inward  toward  the  center  in  all  levels  of  the 
cyclone,  as  was  indicated  in  my  Cloud  Report.  Thus,  the  en- 


tire complex  of  the  circulation  has  dynamic  components,  and 
the  energy  thus  expended  must  be  referred  back  finally  to  the 
source  of  heat  in  the  Tropics,  where  the  absorption  of  radiant 
energy  from  the  sun  goes  on  vigorously  at  the  surface  of  the 
earth.  The  great  general  cyclone  is  perpetuated  by  the  vertical 
uplift  of  the  strata,  due  to  the  residue  of  the  tropical  heat  which 
does  not  leak  out  toward  the  poles  in  horizontal  warm  currents  of 
air  near  the  surface,  and  its  motion  is  in  general  nearly  inde- 
pendent of  the  counterflow  of  these  lower  currents,  except  for 
the  distortion  due  to  the  penetration  just  described.  We  have 
therefore  established  the  existence  in  the  cyclone  of  the  inter- 
action of  three  practically  independent  currents  of  air,  (1)  the 
great  overflowing  eastward  drift,  (2)  the  underflowing  cold 
current  from  the  northwest,  and  (3)  the  underflowing  warm 
stream  from  the  south. 

THE    INTERACTION    OF    THE    THREE    THERMAL    CURRENTS. 

It  is  necessary  yet  further  to  consider  the  thermal  action 
of  these  currents  which  have  very  different  temperatures. 
For  it  is  evident  that  the  formation  of  local  closed  isobars  with 
vortex  action  and  vertical  currents,  while  accompanied  by  dy- 
namic forces  must  yet  depend  upon  a  powerful  and  persistent 
thermal  source.  We  have  elsewhere  shown  that  this  energy 
is  not  to  any  great  extent  the  latent  heat  of  condensation  of 
aqueous  vapor,  this  being  a  secondary  product;  nor  is  the  effect 
purely  dynamic  as  the  eddy  theory  implies.  Where,  then, 
shall  we  find  a  true  efficient  source  of  heat  that  is  competent 
to  account  for  all  the  conditions  observed  in  the  circulation 
phenomena  of  the  atmosphere.  It  seems  to  me  that  this  is  to 
be  attributed  to  the  thermal  action  due  to  the  overflow  of  layers  of 
cold  air  upon  masses  of  warm  air.  Abnormal  stratification  of 
air  currents,  where  the  relatively  cold  is  above  the  warm, 
necessarily  involves  an  upward  current  having  an  energy  pro- 
portional to  the  difference  of  temperature.  It  is  not  necessary 
to  say  more  about  the  truth  of  the  view  that  this  stratification 
exists,  because  such  an  overflow  is  really  one  of  the  most  com- 
mon conditions  to  be  observed  in  meteorology.  If  a  warm 
current  leaves  the  latitudes  of  the  high  pressure  belt,  35° 
more  or  less,  and  runs  northward,  it  begins  to  underflow  the 
eastward  drift.  If  a  cold  area  slides  down  from  the  northwest 
into  warm  latitudes,  its  upper  portions  are  drifted  forward 
over  the  warm  lower  strata.  If  two  currents  counterflow  to- 
gether the  cold  western  masses  are  drifted  forward  upon  the 
warmer  at  moderate  levels,  also  warm  masses  are  carried  east- 
ward over  the  next  anticyclonic  area.  The  instant  the  normal 
thermal  equilibrium  of  the  atmosphere  is  disturbed  by  such 
stratifications,  thermal  energy  is  present  for  the  formation 
of  dynamic  vortices.  Thus  a  hurricane  begins  in  the  late 
summer  when  the  sun  retreating  southward  brings  the  first 
layers  of  cool  air  to  overspread  the  Tropics  in  a  sheet.  The 
warm  surface  air  then  begins  to  flow  under  this  and  penetrates 
it  in  a  vortex,  and  this  continues  to  operate  as  long  as  the  flow 
of  current  sheets  of  two  temperatures  from  the  different  sources 
continues.  The  track  of  a  hurricane  can  thus  traverse  thous- 
ands of  miles,  because  the  cold  overflow  sheet  covers  the  tem- 
perate zone,  and  the  warm  underflow  current  is  directed  in 
streams  depending  upon  the  general  circulation  of  the  lower 
air  about  the  permanent  anticyclonic  centers  of  action.  A 
specific  example  will  make  these  remarks  more  definite. 

In  the  Cloud  Report  we  took  great  pains  to  construct  the 
abnormal  gradients  of  pressure,  temperature,  and  vapor  ten- 
sion, such  as  are  observed  when  the  cumulus  clouds  are  in  the 
process  of  formation.  These  gradients  are  to  be  found  in 
Tables  147,  I  to  VII,  for  the  metric  system,  and  in  Tables  153, 
I  to  VII,  for  the  English  system.  By  entering  these  tables 
with  the  prescribed  arguments  we  can  find  the  gradients  which 
are  prevailing  at  a  given  level  in  a  cyclonic  circulation.  These 
tables  are  constructed  primarily  in  reference  to  the  3500-foot 


35 


plane,  but  they  can  be  extended  to  other  levels  by  the  adjoin- 
ing precepts,  if  some  judgment  is  exercised.  Furthermore,  it 
was  essential  to  establish  the  normal  conditions  which  prevail 
iu  the  atmosphere  at  two  higher  planes,  so  that  the  difference 
between  the  normal  gradients,  which  may  be  readily  computed 
from  the  mean  monthly  values  as  given  in  the  Barometry  Re- 
port, and  the  abnormal  gradients,  which  pertain  to  the  differ- 
ent subareas  of  cyclones  and  anticyclones,  may  be  obtained. 
This  was  one  of  the  purposes  that  was  kept  in  mind  in  con- 
structing the  Barometry  Report,  and  the  data  for  such  normal 
gradients  are  given  in  Table  48.  By  subtracting  the  numerical 
values  for  B,  t,  e,  on  the  different  planes,  and  dividing  by  the 
difference  in  elevation,  these  normal  gradients  are  found.  By 
using  the  surface  data  in  connection  with  the  three  selected 
planes,  we  obtain  several  systems  of  gradients  which  can  thus 
be  computed  for  mutual  comparison.  As  to  the  abnormal 
gradients  of  temperature,  for  example,  we  may  take  from  Table 
153,  II,  of  the  Cloud  Report,  the  values  for  the  different  sub- 
areas  in  a  cyclone,  the  table  being  quoted  only  in  part. 

TABLE  1. — Pressure  and  temperature  gradients  in  English  measures. 
FALL  OF  PRESSURE  IN  INCHES  PER  100  FEET. 


e 
B 

.0100 

.0120 

.0140 

.0160 

.0180 

.0200 

.0220 

.0240 

t  °  F. 

90 

0  095 

0.095 

0.095 

0.096 

0.096 

0.097 

80 

0  096 

097 

.097 

.097 

.097 

.098 

.099 

70 

0  098 

099 

100 

.100 

.101 

.102 

.102 

.103 

60 

102 

103 

104 

.104 

.105 

.  106 

.107 

.108 

50 

105 

106 

107 

.107 

.108 

.109 

.110 

40 

107 

108 

109 

.109 

.110 

.111 

30 

109 

110 

111 

.111 

.112 

20 

113 

114 

115 

.115 

10 

117 

118 

0 

120 

FALL  OF  TEMPERATURE  IN  DEGREES  PER  100  FEET. 


e 
B 

.0100 

.0120 

.0140 

.0160 

.0180 

.0200 

.0220 

.0240 

t  °  F. 

90 

0.88 

0.82 

0.74 

0.240 

80 

0.85 

0.82 

0.74 

.65 

.58 

.52 

.47 

70 

0.79 

.68 

.59 

.51 

.43 

.37 

.34 

.31 

60 

.59 

.48 

.40 

.33 

.30 

.28 

.27 

50 

.41 

.33 

.25 

.20 

40 

.26 

From  Table  153,  International  Cloud  Report. 

In  the  eastern  subareas  we  have  high  temperatures  and  high 
vapor  tensions  (tv  e,)  so  that  the  temperature  gradients  are 
large ;  in  the  western  areas  the  temperatures  and  also  the  vapor 
tensions  are  lower  (tv  e2).  Then  (tv  e,)  will  give  larger  values 
of  G.  tl  than  (f2,  e2)  will  give  for  O.  tf  If  the  Q.  tt  exceeds  the 
normal  gradient  of  the  season,  we  have  the  mechanical  cause 
for  a  vertical  current.  This  principle  can  be  applied  through- 
out the  cyclonic  field  with  unfailing  results  of  the  right  kind. 
In  general  it  may  be  stated  that  the  normal  temperature  gra- 
dients are  about  three-fifths  the  adiabatic  rate,  and  this  occurs 
when  the  strata  are  in  atmospheric  equilibrium  and  no  cur- 
rents are  distinctly  rising  or  falling.  In  cyclones  and  anti- 
cyclones, where  the  vertical  currents  are  pronounced,  the  tem- 
perature gradients  are  about  the  same  as  the  adiabatic  rate. 
This  remarkable  theorem  regarding  gradients  is  very  signifi- 
cant in  the  physical  thermodynamics  of  the  atmosphere. 
Hence,  we  conclude  that  air  is  rising  to  the  east,  but  falling 
to  the  west  of  the  center  of  the  cyclone.  It  seems  almost  a 
paradox  that  in  the  warm  current  of  air  the  air  should  be  rising 
to  a  region  where  the  pressure  is  higher  than  it  was  before 
the  movement  began.  But  rising  air  always  increases  the 


pressure  in  the  stratum  to  which  it  is  moving,  and  this 
hardly  needs  to  be  reaffirmed.  The  overflowing  cold  air  in 
the  strato-cumulus  level,  therefore,  in  itself  generates  the  power 
which  raises  the  warm  air  underneath  it  by  the  usual  thermo- 
dynamic  laws.  Hence,  if  a  relatively  cold  layer  is  thrust  into 
a  column  of  air  otherwise  normally  disposed,  the  warm  lower 
layers  will  rise  to  meet  the  cold  stratum,  and  the  higher  strata 
which  are  also  relatively  warm  will  fall  toward  it.  Relatively 
warm  air  flows  to  the  place  of  relatively  cold  air.  If  the 
surface  layers  are  cooled  by  radiation  in  anticyclones  the  air 
of  the  upper  strata  will  settle  down  upon  them  by  this  law, 
namely,  that  relatively  warm  air  seeks  relatively  cold  air.  The 
currents  of  transfer  thus  set  up  have  an  adiabatic  system  of 
gradients;  on  the  other  hand,  the  normal  layers  of  the  atmos- 
phere do  not  dispose  themselves  into  adiabatic  strata,  as  was 
proved  in  my  Cloud  Report.  Some  specific  examples  of  the 
operation  of  these  processes  will  now  be  mentioned. 

EXAMPLES    OF     THE    INTERACTION    OF    ABNORMALLY   COLD    AND    WARM 

STRATA. 

A  survey  of  the  conditions  prevailing  at  the  time  of  the  water- 
spout photographed  on  August  19,  1896,  off  Cottage  City,  in 
Vineyard  Sound,  Mass.,  leads  me  to  the  results  contained  in 
Table  2,  extracted  from  a  report  now  in  preparation  on  this 
important  phenomenon.  It  contains  for  the  a,  {3,  j-,  3  stages 
the  heights  on  the  photograph  in  millimeters  and  inches,  the 
actual  height  in  meters  and  feet,  and  the  pressure,  tempera- 
ture, and  vapor  tension  at  the  beginning  and  end  of  each  stage. 
Thence  the  gradients  are  found  per  100  meters,  or  per  100  feet, 
viz:  (1)  (O0)  Observed,  according  to  the  actual  observations, 
(2)  (Os)  Cloud,  according  to  the  Cloud  Report  Tables  147  and 
153,  and  (3)  (Gb)  Barometry,  the  normal  gradient  prevailing 
in  the  air  for  that  month  as  deduced  from  Table  48  of  the 
Barometry  Report.  This  waterspout  was  formed  under  re- 
markable conditions.  The  pressure  was  a  little  high,  30.05 
inches;  the  temperature  was  exactly  normal  for  the  month  of 
August,  67.5°  F.,  and  the  vapor  tension  was  low,  correspond- 
ing to  a  relative  humidity  of  64  per  cent.  This  gives  the  ratio 
g 
•j.  =  0.0143  from  which  the  gradients  (Gc),  cloud,  were  obtained. 

Comparing  (G0),  (Gc),  and  (Gb)  we  note  that  (Gb)  is  less  than 
(G0)  and  (<?<,)  in  both  the  pressure  and  the  temperature,  but 
greater  in  the  vapor  tension  for  both  the  a  and  j3  stages.  This 
waterspout  was  formed  in  a  congested  region  on  the  southeast 
edge  of  a  great  area  of  high  pressure,  which  was  pushing 
over  the  New  England  coast  line  at  that  time,  and  there  was 
no  cyclonic  action  of  any  kind.  There  was  then  generated 
a  rapid  formation  of  cumulo-nimbus  clouds,  with  rainfall 
at  the  front,  waterspouts  in  the  middle,  and  thunderstorms 
with  hail  following,  all  in  the  course  of  a  couple  of  hours.  I 
conceive  that  this  entire  set  of  phenomena  was  due  to  the  drift- 
ing forward  (in  the  strato-cumulus  level)  of  the  relatively  cold 
air  of  the  anticyclone  as  a  sheet  overspreading  the  quiet  layers 
of  relatively  warm  air  resting  on  the  ocean.  The  normal  tem- 
perature at  the  ocean  level  is  67.7°  F.  for  August,  and  60.4°  at 
the  3500-foot  level.  But  by  computation  the  temperature  was 
48.7°  at  that  level,  giving  an  abnormal  fall  of  11.7°  F.,  due  to 
the  overflowing  of  the  cold  stratum  from  the  advancing  anti- 
cyclone. This  great  fall  in  temperature  was  not  caused  by  any 
change  in  the  surface  conditions,  which  remained  normal  till  the 
thunderstorm  following  the  rain  and  waterspouts  brought 
the  cold  air  to  the  surface  and  caused  the  temperature  to  fall 
at  the  ocean  also.  The  cold  upper  stratum  evidently  preceded 
the  surface  cold  air  by  several  hours,  and  this  is  typical  of  the 
conditions  frequently  prevailing  in  similar  local  congested  cir- 
culations of  the  lower  strata,  where  abnormal  stratification 
and  so-called  inversion  of  temperature  is  observed.  This  ab- 
normal stratification  of  cold  over  warm  layers  caused  the 


36 


TABLE  2. — Summary  of  the  data  for  the  Cottage  City  waterspout,  August  19,  1896. 


Stages. 

Metric  system. 

English  system. 

II.  photo. 

Height. 

B. 

t 

e. 

H.  photo. 

Height. 

B. 

t. 

e. 

Mm. 
176.4 

Meters. 
4,942 

Mm. 

414.5 

°c. 
—12.0 

Mm. 

1.64 

Inches. 
6.95 

Feet. 
16,  214 

Inches. 
16.32 

»f. 

10.4 

A* 

0.065 

d-stage  .... 

73.6 

2,062 

)  —6.04 
1  —6.  50 

—  0.  582 
—  0.550 

—0.  142 
—0.  140 

2.90 

6,765 

j  —0.  072 
}  —0.  078 

—0.  319 
—0.302 

—0.  00170 
—0.  001G8 

(GJ  Observed. 
(Gc)  Cloud. 

102.8 

2,880 

539.0 

0 

4.57 

4.05 

9,449 

21.22 

32.0 

0.180 

7-stage  

2.6 

74 

—6.76 

0.10 

243 

—0.  082 

100.2 

2,806 

544.0 

0 

4.57 

3.95 

9,206 

21.42 

32.0 

0.180 

/3-stage  

61.7 

1,728 

(  —7.  40 
\  —7.  60 
(  —7.  11 

—  0.538 
—  0.540 
—  0.376 

—0.  240 
—0.  260 
—0.  364 

2.43 

5,669 

(  —0.  089 
-1  —0.  091 
(  —0.  085 

—0.  294 
—0.  294 
—0.  207 

—0.  00288 
—0.00312 
—0.  00437 

(<?0)  Observed. 
(Gy  Cloud. 
(Gb)   Barometry. 

38.5 

1,078 

672.0 

9.3 

8.72 

1.52 

3,537 

26.46 

48.7 

0.343 

a-stage  .... 

38.5 

1,078 

(  —8.  46 
\  —8.  40 
(—8.24 

—  0.  963 
—  0.  950 
—  0.375 

—0.204 
—0.  192 
—0.  296 

1.52 

3,537 

(  —0.  101 
-1  —0.  101 
(—0.098 

—0.  531 
—0.  522 
—0.206 

—0.  00246 
—0.  00230 
—0.  00355 

(<70)  Observed. 
(<?„)  Cloud. 
(Gb)   Barometry. 

Sea  level  .  . 

0 

0 

763.  27 

19.72 

10.92 

0 

0 

30.05 

67.5 

0.430 

thermal  difference  necessary  to  enable  the  hydrostatic  pressure 
of  the  neighboring  region  to  cause  a  vertical  current.  In  this 
rising  air  the  temperature  and  pressure  gradients  changed 
from  the  normal  rates  prevailing  previous  to  the  sudden  change 
into  adiabatic  rates,  which  seem  to  have  been  fully  reached  in 
the  temperature.  There  are  numerous  physical  functions  use- 
ful in  meteorology  involved  in  these  data,  and  it  will  be  valu- 
able to  compute  the  B,  t,  e  in  the  higher  strata  for  as  many 
instances  of  the  kind  as  is  practicable. 

Some  idea  of  the  energy  available  to  produce  a  vertical  cur- 
rent can  be  gained  from  the  following  consideration:  The 
normal  temperature  gradient  in  the  a-stage  is  — 0.206  per  100 
feet,  the  observed  gradient  is  — 0.531,  and  this  is  a  gain  of 
—  0.325.  The  normal  pressure  gradient  is  — 0.098  per  100 
feet,  the  observed  gradient  is  — 0.101,  and  the  gain  is  — 0.003 
per  100  feet,  or  0.106  inch  in  the  a-stage.  That  would  be 
equivalent  to  the  enormous  gradient  of  — 13.5  inches  in  a 
degree,  111,111  meters,  along  the  surface  of  the  earth,  which 
is  100  times  as  great  as  that  observed  for  the  usual  horizontal 
gradients.  In  the  /9-stage  the  temperature  normal  gradient  is 
—  0.207,  the  observed  is  —0.294,  the  increase  —0.087  per  100 
feet.  Comparing  this  with  —  0. 325,  the  increase  in  the  a-stage, 
we  conclude  that  the  efficient  buoyancy  gradient  is  four  times 
greater  in  the  a-stage  than  in  the  /S-stage.  This  is  contrary 
to  what  should  be  expected  if  the  buoyancy  is  chiefly  due  to 
the  condensation  of  aqueous  vapor  to  water  in  the  cloud  or 
/3-stage,  but  it  is  in  accord  with  the  theory  of  stratification 
proposed  in  this  paper. 

We  have  other  examples  of  the  effect  of  an  overflow  of  a 
cold  stratum  upon  the  warm  air  of  lower  levels  in  the  numerous 
cases  where  anticyclonic  areas  advance  into  the  central  val- 
leys from  the  northwest  without  a  cyclonic  development  in 
front  of  them.  There  is  produced  in  such  conditions  a  wide 
band  of  rainfall  on  the  map,  stretching  from  the  Lake  region 
to  the  Gulf  of  Mexico,  where  no  dynamic  action  is  operating 
which  can  raise  the  air  mechanically.  The  cold,  overflowing 
sheet  will,  however,  cause  an  increase  in  the  temperature 
gradient,  and  this  is  accompanied  by  rising  air  and  precipita- 
tion over  immense  areas  of  country.  In  certain  cases  the  anti- 


cyclonic  area  will  advance  to  the  Atlantic  coast  before  causing 
such  ascending  currents,  and  then  a  powerful  small  cyclone 
sometimes  develops  suddenly  near  the  coast  of  New  Jersey  or 
Virginia,  and  as  this  advances  to  New  England  it  produces  hur- 
ricane winds.  When  two  currents  of  different  temperatures 
flow  together  in  the  Mississippi  Valley  the  overflow  of  the  cold 
layers  from  the  northwest  upon  the  warm  layers  from  the 
south  produces  a  congested  condition,  accompanied  by  thun- 
derstorms, tornadoes,  and  general  violent  local  circulations  in 
the  southeastern  quadrants  of  the  cyclone.  On  the  other  hand, 
the  wide  range  in  temperature  required  to  cause  such  rapid 
vertical  circulations  may  also  be  produced  by  simply  over- 
heating the  surface  layers  relatively  to  the  upper  strata. 
This  is  the  case  in  summer,  when  in  anticyclonic  areas  the 
solar  radiation  passes  through  all  the  upper  layers  to  the  sur- 
face without  heating  them  sensibly.  Then  the  earth's  radia- 
tion, in  its  turn,  does  have  the  power  to  overheat  the  lower 
strata,  and  this  causes  an  increased  temperature  gradient  rela- 
tively to  the  cumulus  levels,  which  is  the  atmospheric  con- 
dition for  numerous  summer  thunderstorms  and  desert  sand 
squalls.  In  the  winter  the  areas  of  low  pressure  over  the 
northern  portions  of  the  Atlantic  and  Pacific  oceans  are  due 
to  the  relatively  high  temperature  of  the  ocean  waters  and 
adjacent  air  layers.  During  the  months  in  which  the  lower 
layers  are  too  warm  in  comparison  with  the  adjacent  conti- 
nental areas  and  with  the  strata  above  them,  the  well-known 
.permanent  cyclones  prevail.  The  reverse  case  occurs  in  sum- 
mer over  the  ocean  belts  at  the  boundary  of  the  tropical  and 
the  temperate  zones,  where  the  water  holds  the  surface  strata 
at  temperatures  lower  than  is  required  for  equilibrium,  and 
so  causes  a  settling  down  of  the  upper  air.  This  is,  of  course, 
an  effect  which  increases  the  usual  dynamic  action  produced 
by  the  general  circulation  in  this  high  pressure  belt. 

In  the  autumn  the  cold  layers  advance  from  the  northern 
zones  into  the  Tropics,  first  in  the  higher  strata  which  over- 
spread the  warm  and  moist  air  of  the  doldrums.  This  causes  an 
increase  of  the  vertical  temperature  gradient,  and  a  hurricane  or 
large  columnar  vortex  is  formed,  through  whose  structure  the 
warm  air  pours  upward  to  great  heights,  and  enables  this  con- 


37 


figuration  in  some  cases  to  perpetuate  itself  by  such  convection 
for  many  days.  It  is  the  wide  spread  cold  sheet  of  the  upper 
strata  which  is  the  persistent  source  of  energy  in  a  hurricane, 
and  also  in  a  cyclone.  The  advancing  movement  of  the  center 
is  due  to  the  fact  that  the  warm  air,  which  lies  to  the  eastward, 
promptly  rises  to  meet  the  overflowing  cold  sheet,  the  two 
mutually  sustaining  each  other's  action.  The  downflow  of  the 
cold  air  on  the  western  side  is  simultaneous  with  the  upflow 
on  the  eastern  side,  but  the  deficiency  of  pressure  on  one  side 
and  the  excess  of  it  on  the  other  by  its  continuous  opera- 
tion causes  the  entire  structure  to  advance.  In  addition  to 
this,  the  drift  of  the  upper  strata,  eastward  in  the  temperate 
zone  and  westward  in  the  Tropics,  carries  along  the  cyclone, 
which  adheres  to  them  by  the  interactions  that  have  been 
described. 

GENERAL   RESULTS    STATED. 

The  results  of  this  research  may  be  summed  up  briefly  as 
follows:  (1)  The  cyclone  is  not  formed  from  the  energy  of  the 
latent  heat  of  condensation,  however  much  this  may  strengthen 
its  intensity;  it  is  not  an  eddy  in  the  eastward  drift;  but  it  is 
caused  by  the  counterflow  and  overflow  of  currents  of  different 
temperatures.  Ferrel's  canal  theory  of  the  general  circulation 
is  not  sustained  by  the  observations,  nor  is  his  theory  of  local 
cyclones  and  anticyclones  tenable.  There  are  difficulties  with 
regard  to  the  German  vortex  theory,  but  this  is  nearer  the 
truth  than  the  Ferrel  vortex.  The  structure  in  nature  is 


actually  more  complex  than  has  been  admitted  in  these  theo- 
retical discussions,  but  it  doubtless  can  be  worked  out  suc- 
cessfully along  the  lines  herein  indicated.  (2)  Regarding  the 
relation  of  the  upper  level  isobars  to  practical  forecasting,  it 
is  noted  as  the  result  of  the  examination  of  the  charts  of 
December,  1902,  January  and  February,  1903,  that  (a)  the 
direction  of  the  advance  of  the  center  of  the  low  pressure 
is  controlled  by  the  upper  strata,  and  its  track  for  the  fol- 
lowing twenty-four  hours  is  usually  indicated  by  the  posi- 
tion of  the  10,000-foot  level  isobars;  (6)  The  velocity  of  the 
daily  motion  is  also  dependent  upon  and  is  shown  by  the 
density  of  these  high  level  isobars;  (c)  the  penetrating  power 
of  the  cyclone  is  safely  inferred  from  an  inspection  of  the 
three  maps  of  isobars  of  the  same  date;  (d)  there  is  decided 
evidence  that  areas  of  precipitation  occur  where  the  3500-foot 
isobars  and  the  10,000-foot  isobars  cross  each  other  at  an 
angle  in  the  neighborhood  of  90° ;  (e)  there  have  been  several 
cases  in  which  the  formation  of  a  new  cyclone  has  been  first 
distinctly  shown  on  the  upper  system  of  isobars  before  pene- 
trating to  the  surface  or  making  itself  evident  at  the  sea  level. 
(3)  It  is  expected  that  by  completing  our  discussion  of  the 
temperature  gradients  between  the  surface  and  the  higher 
levels  we  shall  be  able  to  secure  daily  isotherms  as  well  as 
daily  isobars  on  the  upper  planes,  and  this  will  tend  to 
strengthen  any  further  examination  of  these  important  prob- 
lems. A  suitable  report  will  be  prepared  in  which  the  data 
now  coming  into  our  possession  will  be  subjected  to  a  mathe- 
matical analysis  and  discussion. 


1 

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